Means of Hilbert Space Operators

Means of Hilbert Space Operators
Title Means of Hilbert Space Operators PDF eBook
Author Fumio Hiai
Publisher Springer
Pages 151
Release 2003-12-09
Genre Mathematics
ISBN 3540451528

Download Means of Hilbert Space Operators Book in PDF, Epub and Kindle

The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.

Means of Hilbert Space Operators

Means of Hilbert Space Operators
Title Means of Hilbert Space Operators PDF eBook
Author Fumio Hiai
Publisher Springer Science & Business Media
Pages 164
Release 2002
Genre
ISBN 9783540406808

Download Means of Hilbert Space Operators Book in PDF, Epub and Kindle

Numerical Ranges of Hilbert Space Operators

Numerical Ranges of Hilbert Space Operators
Title Numerical Ranges of Hilbert Space Operators PDF eBook
Author Hwa-Long Gau
Publisher Cambridge University Press
Pages 556
Release 2021-08-05
Genre Mathematics
ISBN 1108787606

Download Numerical Ranges of Hilbert Space Operators Book in PDF, Epub and Kindle

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.

An Introduction to Models and Decompositions in Operator Theory

An Introduction to Models and Decompositions in Operator Theory
Title An Introduction to Models and Decompositions in Operator Theory PDF eBook
Author Carlos S. Kubrusly
Publisher Springer Science & Business Media
Pages 152
Release 1997-08-19
Genre Mathematics
ISBN 9780817639921

Download An Introduction to Models and Decompositions in Operator Theory Book in PDF, Epub and Kindle

By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.

A Glimpse at Hilbert Space Operators

A Glimpse at Hilbert Space Operators
Title A Glimpse at Hilbert Space Operators PDF eBook
Author Sheldon Axler
Publisher Springer Science & Business Media
Pages 360
Release 2011-04-13
Genre Mathematics
ISBN 3034603479

Download A Glimpse at Hilbert Space Operators Book in PDF, Epub and Kindle

Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.

Operator Analysis

Operator Analysis
Title Operator Analysis PDF eBook
Author Jim Agler
Publisher Cambridge University Press
Pages 393
Release 2020-03-26
Genre Mathematics
ISBN 1108485448

Download Operator Analysis Book in PDF, Epub and Kindle

This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.

Operators on Hilbert Space

Operators on Hilbert Space
Title Operators on Hilbert Space PDF eBook
Author V. S. Sunder
Publisher Springer
Pages 107
Release 2016-08-05
Genre Mathematics
ISBN 9811018162

Download Operators on Hilbert Space Book in PDF, Epub and Kindle

The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.