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The Numerical Range And The Core Of Hilbert Space Operators Microform
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Author :Ching-Nam Hung Publisher :Library and Archives Canada = Bibliothèque et Archives Canada ISBN 13 :9780612944039 Total Pages :160 pages Book Rating :4.9/5 (44 download)
Book Synopsis The Numerical Range and the Core of Hilbert-space Operators [microform] by : Ching-Nam Hung
Download or read book The Numerical Range and the Core of Hilbert-space Operators [microform] written by Ching-Nam Hung and published by Library and Archives Canada = Bibliothèque et Archives Canada. This book was released on 2004 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main object of this thesis is to study the numerical range of Hilbert-space operators. In 1973, T. Ando examined the geometric and algebraic properties of operators and developed a structure theory. In continuation of his work, there has been much progress, especially in the study of the core of a numerical contraction in terms of dilation theory and representation theory. In the first half of this thesis, explicit expressions for the minimum and the maximum of the core of a numerical contraction are studied. The expressions for these extremals are given as strongly convergent non-commutative operator series in terms of the given numerical contraction and its adjoint. This part of the thesis serves as a complement to T. Ando's theorem, in which we find that the operator series provides an efficient mechanism for writing a numerical contraction in terms of dilations and representations. The main tool employed is the theory of Schur complements of positive semi-definite operator matrices. Further discussions on the classical Catalan problem and another related combinatorial problem are also presented. In the second half of this thesis, matrices whose numerical ranges are the closed unit disc are investigated, and the structural expressions of those matrices are studied. As a result, matrices having elliptical discs as numerical range are found to possess the property that the foci of the disc are their eigenvalues. The structure theory obtained by T. Ando, especially the representation of numerical contractions, is essential in proving these results. Finally, the structural expressions of matrices with numerical range equal to the closed unit disc are used to provide an alternative proof for P.Y. Wu's theorem concerning the norms of matrices.
Book Synopsis Numerical Ranges of Hilbert Space Operators by : Hwa-Long Gau
Download or read book Numerical Ranges of Hilbert Space Operators written by Hwa-Long Gau and published by Cambridge University Press. This book was released on 2021-08-05 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.
Author :Silvestru Sever Dragomir Publisher :Springer Science & Business Media ISBN 13 :331901448X Total Pages :130 pages Book Rating :4.3/5 (19 download)
Book Synopsis Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces by : Silvestru Sever Dragomir
Download or read book Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces written by Silvestru Sever Dragomir and published by Springer Science & Business Media. This book was released on 2013-09-14 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.
Book Synopsis Joint Numerical Range and Joint Spectrum of Hilbert Space Operators by : Nicolaas Pieter Dekker
Download or read book Joint Numerical Range and Joint Spectrum of Hilbert Space Operators written by Nicolaas Pieter Dekker and published by . This book was released on 1969 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras by : F. F. Bonsall
Download or read book Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by F. F. Bonsall and published by CUP Archive. This book was released on 1971-03-02 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures.
Book Synopsis Numerical Ranges and Commutation Properties of Hilbert Space Operators by : Bruce Kent Richard
Download or read book Numerical Ranges and Commutation Properties of Hilbert Space Operators written by Bruce Kent Richard and published by . This book was released on 1974 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Numerical Range of a Bounded Linear Operator in Hilbert Space by : Ronald Ricardo Abderhalden
Download or read book On the Numerical Range of a Bounded Linear Operator in Hilbert Space written by Ronald Ricardo Abderhalden and published by . This book was released on 1968 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Joint numerical range and joint spectrum of hilbert space opera... by : Nicolaas Pieter Dekker
Download or read book Joint numerical range and joint spectrum of hilbert space opera... written by Nicolaas Pieter Dekker and published by . This book was released on 19?? with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invitation to Linear Operators by : Takayuki Furuta
Download or read book Invitation to Linear Operators written by Takayuki Furuta and published by CRC Press. This book was released on 2001-07-26 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a Hilbert space. The author first states the important properties of a Hilbert space, then sets out the fundamental properties of bounded linear operators on a Hilbert space. The final section presents some of the more recent developments in bounded linear operators.
Book Synopsis Commutation Properties of Hilbert Space Operators, and Related Topics by : Calvin Richard Putnam
Download or read book Commutation Properties of Hilbert Space Operators, and Related Topics written by Calvin Richard Putnam and published by . This book was released on 1967 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: What could be regarded as the beginning of a theory of commutators AB - BA of operators A and B on a Hilbert space, considered as a dis cipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commuta tion relations occurring there. Here A and B were unbounded self-adjoint operators satisfying the relation AB - BA = iI, in some appropriate sense, and the problem was that of establishing the essential uniqueness of the pair A and B. The study of commutators of bounded operators on a Hilbert space has a more recent origin, which can probably be pinpointed as the paper of Wintner [6] {1947}. An investigation of a few related topics in the subject is the main concern of this brief monograph. The ensuing work considers commuting or "almost" commuting quantities A and B, usually bounded or unbounded operators on a Hilbert space, but occasionally regarded as elements of some normed space. An attempt is made to stress the role of the commutator AB - BA, and to investigate its properties, as well as those of its components A and B when the latter are subject to various restrictions. Some applica tions of the results obtained are made to quantum mechanics, perturba tion theory, Laurent and Toeplitz operators, singular integral trans formations, and Jacobi matrices.
Book Synopsis An Introduction to Operators on the Hardy-Hilbert Space by : Ruben A. Martinez-Avendano
Download or read book An Introduction to Operators on the Hardy-Hilbert Space written by Ruben A. Martinez-Avendano and published by Springer Science & Business Media. This book was released on 2007 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of analytic functions and of operators on them. The goal is to provide an elementary and engaging introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis. The exposition, blending techniques from "soft" and "hard" analysis, is intended to be as clear and instructive as possible. Many of the proofs are very elegant. This book evolved from a graduate course that was taught at the University of Toronto. It should prove suitable as a textbook for beginning graduate students, or even for well-prepared advanced undergraduates, as well as for independent study. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Book Synopsis Range Characterization, Fatorization of Hilbert Space Operators by : Ernesto Jaimes
Download or read book Range Characterization, Fatorization of Hilbert Space Operators written by Ernesto Jaimes and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis K-numerical Ranges of Operators on Hilbert Spaces by : B. Nashvadian Bakhsh
Download or read book K-numerical Ranges of Operators on Hilbert Spaces written by B. Nashvadian Bakhsh and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hilbert Space Operators by : J. M. Bachar
Download or read book Hilbert Space Operators written by J. M. Bachar and published by . This book was released on 2014-01-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hilbert Space Operators by : John M. Bachar
Download or read book Hilbert Space Operators written by John M. Bachar and published by Springer. This book was released on 1978 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Means of Hilbert Space Operators by : Fumio Hiai
Download or read book Means of Hilbert Space Operators written by Fumio Hiai and published by . This book was released on 2014-01-15 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Compressions of Unbounded Normal Hilbert Space Operators by : John Michael Hosack
Download or read book Compressions of Unbounded Normal Hilbert Space Operators written by John Michael Hosack and published by . This book was released on 1968 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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