Numerical Ranges Of Hilbert Space Operators
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Numerical Ranges Of Hilbert Space Operators
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Author : Hwa-Long Gau
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-31
Numerical Ranges Of Hilbert Space Operators written by Hwa-Long Gau and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-31 with Mathematics categories.
Numerical Ranges Of Hilbert Space Operators
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Author : Hwa-Long Gau
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-05
Numerical Ranges Of Hilbert Space Operators written by Hwa-Long Gau and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-05 with Mathematics categories.
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.
Numerical Range
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Author : Karl E. Gustafson
language : en
Publisher: Springer
Release Date : 1996-11-07
Numerical Range written by Karl E. Gustafson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-07 with Mathematics categories.
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
A Hilbert Space Problem Book
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Author : P.R. Halmos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Hilbert Space Problem Book written by P.R. Halmos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Numerical Ranges And Commutation Properties Of Hilbert Space Operators
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Author : Bruce Kent Richard
language : en
Publisher:
Release Date : 1974
Numerical Ranges And Commutation Properties Of Hilbert Space Operators written by Bruce Kent Richard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Invitation To Linear Operators
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Author : Takayuki Furuta
language : en
Publisher: CRC Press
Release Date : 2001-07-26
Invitation To Linear Operators written by Takayuki Furuta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-26 with Mathematics categories.
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.
The Numerical Range And The Core Of Hilbert Space Operators Microform
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Author : Ching-Nam Hung
language : en
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
Release Date : 2004
The Numerical Range And The Core Of Hilbert Space Operators Microform written by Ching-Nam Hung and has been published by Library and Archives Canada = Bibliothèque et Archives Canada this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
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.
Numerical Range
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Author : Karl E. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Range written by Karl E. Gustafson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
Numerical Ranges Of Operators On Normed Spaces And Of Elements Of Normed Algebras
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Author : F. F. Bonsall
language : en
Publisher: CUP Archive
Release Date : 1971-03-02
Numerical Ranges Of Operators On Normed Spaces And Of Elements Of Normed Algebras written by F. F. Bonsall and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-03-02 with Mathematics categories.
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.
An Operator Theory Problem Book
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Author : Mohammed Hichem Mortad
language : en
Publisher:
Release Date : 2018
An Operator Theory Problem Book written by Mohammed Hichem Mortad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.