Spectral Properties Of Certain Operators On A Free Hilbert Space And The Semicircular Law PDF Download
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| Author | : Ilwoo Cho |
| Publisher | : Elsevier |
| Total Pages | : 166 |
| Release | : 2023-04-21 |
| Genre | : Mathematics |
| ISBN | : 0443151768 |
Download Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law Book in PDF, ePub and Kindle
In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and operators acting on them. The construction of these operators itself is interesting and provides new types of Hilbert-space operators. Also, by considering spectral-theoretic properties of these operators, the authors illustrate how “free-Hilbert-space Operator Theory is different from the classical Operator Theory. More interestingly, the authors demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how “inside actions of operator algebra deform the free-probabilistic information—in particular, the semicircular law. Presents the spectral properties of three types of operators on a Hilbert space, in particular how these operators affect the semicircular law Demonstrates how the semicircular law is deformed by actions "from inside", as opposed to actions "from outside" considered by previous theory Explores free Hilbert spaces and their modeling applications Authored by two leading researchers in Operator Theory and Operator Algebra
| Author | : K. B. Laursen |
| Publisher | : Oxford University Press |
| Total Pages | : 610 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780198523819 |
Download An Introduction to Local Spectral Theory Book in PDF, ePub and Kindle
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
| Author | : Kurt O. Friedrichs |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461263964 |
Download Spectral Theory of Operators in Hilbert Space Book in PDF, ePub and Kindle
The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. The guiding notion in this approach is that of spectral representation. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra. The preparation of the original version of these lecture notes was greatly helped by the assistance of P. Rejto. Various valuable suggestions made by him and by R. Lewis have been incorporated. The present version of the notes contains extensive modifica tions, in particular in the chapters on bounded and unbounded operators. February, 1973 K.O.F. PREFACE TO THE SECOND PRINTING The second printing (1980) is a basically unchanged reprint in which a number of minor errors were corrected. The author wishes to thank Klaus Schmidt (Lausanne) and John Sylvester (New York) for their lists of errors. v TABLE OF CONTENTS I. Spectral Representation 1 1. Three typical problems 1 12 2. Linear space and functional representation.
| Author | : Pietro Aiena |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 452 |
| Release | : 2007-05-08 |
| Genre | : Mathematics |
| ISBN | : 1402025254 |
Download Fredholm and Local Spectral Theory, with Applications to Multipliers Book in PDF, ePub and Kindle
A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.
| Author | : Gilbert Helmberg |
| Publisher | : Courier Dover Publications |
| Total Pages | : 370 |
| Release | : 2008-06-11 |
| Genre | : Science |
| ISBN | : 0486466221 |
Download Introduction to Spectral Theory in Hilbert Space Book in PDF, ePub and Kindle
This introduction to Hilbert space, bounded self-adjoint operators, the spectrum of an operator, and operators' spectral decomposition is accessible to readers familiar with analysis and analytic geometry. 1969 edition.
| Author | : Ion Colojoara |
| Publisher | : CRC Press |
| Total Pages | : 254 |
| Release | : 1968 |
| Genre | : Mathematics |
| ISBN | : 9780677014807 |
Download Theory of Generalized Spectral Operators Book in PDF, ePub and Kindle
| Author | : Carlos S. Kubrusly |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 203 |
| Release | : 2012-06-01 |
| Genre | : Mathematics |
| ISBN | : 0817683283 |
Download Spectral Theory of Operators on Hilbert Spaces Book in PDF, ePub and Kindle
This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field.
| Author | : A. A. Balinsky |
| Publisher | : World Scientific |
| Total Pages | : 200 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 1848162189 |
Download Spectral Analysis of Relativistic Operators Book in PDF, ePub and Kindle
Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances.This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992.
| Author | : Kurt Otto Friedrichs |
| Publisher | : |
| Total Pages | : 244 |
| Release | : 1980 |
| Genre | : |
| ISBN | : |
Download Spectral Theory of Operators in Hilbert Space Book in PDF, ePub and Kindle
| Author | : Christiane Tretter |
| Publisher | : World Scientific |
| Total Pages | : 297 |
| Release | : 2008 |
| Genre | : Science |
| ISBN | : 1860947689 |
Download Spectral Theory of Block Operator Matrices and Applications Book in PDF, ePub and Kindle
This book presents new concepts in operator theory and covers classes of operators (in particular, non-selfadjoint operators) which exhibit various interesting phenomena. Special attention is paid to applications in many areas of mathematical physics, including quantum mechanics, fluid mechanics, and magnetohydrodynamics.The author also discusses an operator theoretic approach to spectral problems for linear operators admitting a certain block structure. The results apply to bounded or finite-dimensional operators like block matrices as well to unbounded operators describing systems of differential equations. New concepts of numerical range are developed.
