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Projective And Injective Banach Spaces
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Book Synopsis Separably Injective Banach Spaces by : Antonio Avilés
Download or read book Separably Injective Banach Spaces written by Antonio Avilés and published by Springer. This book was released on 2016-03-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.
Book Synopsis Introduction to Tensor Products of Banach Spaces by : Raymond A. Ryan
Download or read book Introduction to Tensor Products of Banach Spaces written by Raymond A. Ryan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first ever truly introductory text to the theory of tensor products of Banach spaces. Coverage includes a full treatment of the Grothendieck theory of tensor norms, approximation property and the Radon-Nikodym Property, Bochner and Pettis integrals. Each chapter contains worked examples and a set of exercises, and two appendices offer material on summability in Banach spaces and properties of spaces of measures.
Book Synopsis Handbook of the Geometry of Banach Spaces by :
Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces
Book Synopsis Homological Methods in Banach Space Theory by : Félix Cabello Sánchez
Download or read book Homological Methods in Banach Space Theory written by Félix Cabello Sánchez and published by Cambridge University Press. This book was released on 2023-01-31 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.
Book Synopsis Encyclopedic Dictionary of Mathematics by : Nihon Sūgakkai
Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.
Book Synopsis Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras by : Theodore W. Palmer
Download or read book Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras written by Theodore W. Palmer and published by Cambridge University Press. This book was released on 1994-03-25 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.
Book Synopsis Factorization of Linear Operators and Geometry of Banach Spaces by : Gilles Pisier
Download or read book Factorization of Linear Operators and Geometry of Banach Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1986 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25-29, 1984"--T.p. verso.
Book Synopsis Trends in Banach Spaces and Operator Theory by : Anna Kamińska
Download or read book Trends in Banach Spaces and Operator Theory written by Anna Kamińska and published by American Mathematical Soc.. This book was released on 2003 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.
Book Synopsis Pseudo-Differential Operators and Symmetries by : Michael Ruzhansky
Download or read book Pseudo-Differential Operators and Symmetries written by Michael Ruzhansky and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.
Book Synopsis Boletín de la Sociedad Matemática Mexicana by : Sociedad Matemática Mexicana
Download or read book Boletín de la Sociedad Matemática Mexicana written by Sociedad Matemática Mexicana and published by . This book was released on 2003 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear and Complex Analysis Problem Book 3 by : Victor P. Havin
Download or read book Linear and Complex Analysis Problem Book 3 written by Victor P. Havin and published by Springer. This book was released on 2006-12-08 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!
Book Synopsis On the Algebraic Foundations of Bounded Cohomology by : Theo Bühler
Download or read book On the Algebraic Foundations of Bounded Cohomology written by Theo Bühler and published by American Mathematical Soc.. This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a widespread opinion among experts that (continuous) bounded cohomology cannot be interpreted as a derived functor and that triangulated methods break down. The author proves that this is wrong. He uses the formalism of exact categories and their derived categories in order to construct a classical derived functor on the category of Banach $G$-modules with values in Waelbroeck's abelian category. This gives us an axiomatic characterization of this theory for free, and it is a simple matter to reconstruct the classical semi-normed cohomology spaces out of Waelbroeck's category. The author proves that the derived categories of right bounded and of left bounded complexes of Banach $G$-modules are equivalent to the derived category of two abelian categories (one for each boundedness condition), a consequence of the theory of abstract truncation and hearts of $t$-structures. Moreover, he proves that the derived categories of Banach $G$-modules can be constructed as the homotopy categories of model structures on the categories of chain complexes of Banach $G$-modules, thus proving that the theory fits into yet another standard framework of homological and homotopical algebra.
Book Synopsis Theory of Operator Spaces by : Edward G. Effros
Download or read book Theory of Operator Spaces written by Edward G. Effros and published by American Mathematical Society. This book was released on 2022-03-25 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the main results and ideas in the theories of completely bounded maps, operator spaces, and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis to read through the book. The descriptions and discussions of the topics are self-explained. It is appropriate for graduate students new to the subject and the field. The book starts with the basic representation theorems for abstract operator spaces and their mappings, followed by a discussion of tensor products and the analogue of Grothendieck's approximation property. Next, the operator space analogues of the nuclear, integral, and absolutely summing mappings are discussed. In what is perhaps the deepest part of the book, the authors present the remarkable “non-classical” phenomena that occur when one considers local reflexivity and exactness for operator spaces. This is an area of great beauty and depth, and it represents one of the triumphs of the subject. In the final part of the book, the authors consider applications to non-commutative harmonic analysis and non-self-adjoint operator algebra theory. Operator space theory provides a synthesis of Banach space theory with the non-commuting variables of operator algebra theory, and it has led to exciting new approaches in both disciplines. This book is an indispensable introduction to the theory of operator spaces.
Book Synopsis Lectures on Amenability by : Volker Runde
Download or read book Lectures on Amenability written by Volker Runde and published by Springer. This book was released on 2004-10-12 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.
Book Synopsis Higher Moments of Banach Space Valued Random Variables by : Svante Janson
Download or read book Higher Moments of Banach Space Valued Random Variables written by Svante Janson and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.
Book Synopsis Injective Banach Spaces of Type C(T) by : John Edwin Wolfe
Download or read book Injective Banach Spaces of Type C(T) written by John Edwin Wolfe and published by . This book was released on 1971 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Functional Analysis by : Reinhold Meise
Download or read book Introduction to Functional Analysis written by Reinhold Meise and published by Clarendon Press. This book was released on 1997-07-31 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces it proceeds quickly to the central results of the field, including the theorem of HahnBanach. The spaces (p Lp (X,(), C(X)' and Sobolov spaces are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C*-algebras and the spectral representation for bounded normal and unbounded self-adjoint operators in Hilbert spaces. An introduction to locally convex spaces and their duality theory provides the basis for a comprehensive treatment of Fr--eacute--;chet spaces and their duals. In particular recent results on sequences spaces, linear topological invariants and short exact sequences of Fr--eacute--;chet spaces and the splitting of such sequences are presented. These results are not contained in any other book in this field.
