Modern Approaches to the Invariant-Subspace Problem PDF Download
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Author: Isabelle Chalendar
Publisher: Cambridge University Press
ISBN: 1139503294
Category : Mathematics
Languages : en
Pages : 298
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Book Description
One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Author: Isabelle Chalendar
Publisher: Cambridge University Press
ISBN: 1139503294
Category : Mathematics
Languages : en
Pages : 298
Get Book Here
Book Description
One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Author: Isabelle Chalendar
Publisher:
ISBN: 9781139128605
Category : MATHEMATICS
Languages : en
Pages : 298
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Book Description
Presents work on the invariant subspace problem, a major unsolved problem in operator theory.
Author: Fernanda Botelho
Publisher: American Mathematical Soc.
ISBN: 1470427729
Category : Mathematics
Languages : en
Pages : 250
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Book Description
This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15–16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17–18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their “nice” spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.
Author: Richard M. Aron
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110656752
Category : Mathematics
Languages : en
Pages : 364
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Book Description
The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside’s theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.
Author: Mortad Mohammed Hichem
Publisher: World Scientific
ISBN: 9813236272
Category : Mathematics
Languages : en
Pages : 656
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Book Description
This book is for third and fourth year university mathematics students (and Master students) as well as lecturers and tutors in mathematics and anyone who needs the basic facts on Operator Theory (e.g. Quantum Mechanists). The main setting for bounded linear operators here is a Hilbert space. There is, however, a generous part on General Functional Analysis (not too advanced though). There is also a chapter on Unbounded Closed Operators.The book is divided into two parts. The first part contains essential background on all of the covered topics with the sections: True or False Questions, Exercises, Tests and More Exercises. In the second part, readers may find answers and detailed solutions to the True or False Questions, Exercises and Tests.Another virtue of the book is the variety of the topics and the exercises and the way they are tackled. In many cases, the approaches are different from what is known in the literature. Also, some very recent results from research papers are included.
Author: Damian Betebenner
Publisher:
ISBN:
Category : Invariant subspaces
Languages : en
Pages : 148
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Book Description
Author: Joel H. Shapiro
Publisher: American Mathematical Soc.
ISBN: 1470441160
Category : Convolutions (Mathematics)
Languages : en
Pages : 219
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Book Description
This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques—all in the pursuit of two celebrated results: the Titchmarsh Convolution Theorem and the Volterra Invariant Subspace Theorem. Exercises throughout the text enhance the material and facilitate interactive study.
Author: Joel H. Shapiro
Publisher: Springer
ISBN: 3319279785
Category : Mathematics
Languages : en
Pages : 225
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Book Description
This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll–Nardzewski surrounding fixed points for families of affine maps.
Author: Fabrizio Colombo
Publisher: Birkhäuser
ISBN: 3319623621
Category : Mathematics
Languages : en
Pages : 398
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Book Description
This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.
Author:
Publisher: Oxford University Press
ISBN: 019286386X
Category : Operator theory
Languages : en
Pages : 529
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Book Description
Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.
