Hari Bercovici's Books

Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics

The Carl M. Pearcy Anniversary Volume

By: Hari Bercovici

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Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics

The Carl M. Pearcy Anniversary Volume

By: Hari Bercovici

This volume, dedicated to Carl Pearcy on the occasion of his 60th birthday, presents recent results in operator theory, nonselfadjoint operator algebras, measure theory and the theory of moments. The articles on these subjects have been contributed by leading area experts, many of whom were associated with Carl Pearcy as students or collaborators.

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Page Count

228

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764359544

ISBN 13

9783764359546

Recent Advances in Operator Theory and Operator Algebras

By: Hari Bercovici,Elias Katsoulis,David Kerr,Dan Timotin

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Recent Advances in Operator Theory and Operator Algebras

By: Hari Bercovici,Elias Katsoulis,David Kerr,Dan Timotin

This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.

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Page Count

167

Publisher

CRC Press

Published Date

ISBN 10

1317974611

ISBN 13

9781317974611

Measure and Integration

By: Hari Bercovici,Arlen Brown,Carl Pearcy

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Measure and Integration

By: Hari Bercovici,Arlen Brown,Carl Pearcy

This book covers the material of a one year course in real analysis. It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom. Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text. Hints are included for some of the more difficult problems.

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Page Count

306

Publisher

Springer

Published Date

ISBN 10

3319290460

ISBN 13

9783319290461

Operator Theory and Arithmetic in H [infinity]

By: Hari Bercovici

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Operator Theory and Arithmetic in H [infinity]

By: Hari Bercovici

Jordan's classification theorem for linear transformations on a finite-dimensional vector space is a natural highlight of the deep relationship between linear algebra and the arithmetical properties of polynomial rings. Because the methods and results of finite-dimensional linear algebra seldom extend to or have analogs in infinite-dimensional operator theory, it is therefore remarkable to have a class of operators which has a classification theorem analogous to Jordan's classical result and has properties closely related to the arithmetic of the ring $H^{\infty}$ of bounded analytic functions in the unit disk. $C_0$ is such a class and is the central object of study in this book.A contraction operator belongs to $C_0$ if and only if the associated functional calculus on $H^{\infty}$ has a nontrivial kernel. $C_0$ was discovered by Bela Sz.-Nagy and Ciprian Foias in their work on canonical models for contraction operators on Hilbert space. Besides their intrinsic interest and direct applications, operators of class $C_0$ are very helpful in constructing examples and counterexamples in other branches of operator theory. In addition, $C_0$ arises in certain problems of control and realization theory.In this survey work, the author provides a unified and concise presentation of a subject that was covered in many articles. The book describes the classification theory of $C_0$ and relates this class to other subjects such as general dilation theory, stochastic realization, representations of convolution algebras, and Fredholm theory. This book should be of interest to operator theorists as well as theoretical engineers interested in the applications of operator theory. In an effort to make the book as self-contained as possible, the author gives an introduction to the theory of dilations and functional models for contraction operators. Prerequisites for this book are a course in functional analysis and an acquaintance with the theory of Hardy spaces in the unit disk. In addition, knowledge of the trace class of operators is necessary in the chapter on weak contractions.

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Page Count

289

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821815288

ISBN 13

9780821815281

Harmonic Analysis of Operators on Hilbert Space

By: Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy

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Harmonic Analysis of Operators on Hilbert Space

By: Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

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Page Count

482

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441960945

ISBN 13

9781441960948

Operator Theory and Interpolation

International Workshop on Operator Theory and Applications, IWOTA 96

By: Hari Bercovici,Ciprian Foiaş

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Operator Theory and Interpolation

International Workshop on Operator Theory and Applications, IWOTA 96

By: Hari Bercovici,Ciprian Foiaş

Systems and control theories use sophisticated operator theoretical methods. They also provide new ideas and problems in operator theory." "The articles in this volume originated from the IWOTA conference held at Indiana University, Bloomington, in June 1996. They represent most of the areas that were discussed at the workshop with some emphasis on modern interpolation theory, a topic which has seen much progress in recent years."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

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