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Invitation To Linear Operators

Author: Takayuki Furuta
Publisher: CRC Press
ISBN: 9780415267991
Size: 77.29 MB
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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.

Spectral Theory Of Block Operator Matrices And Applications

Author: Christiane Tretter
Publisher: World Scientific
ISBN: 1908979321
Size: 31.48 MB
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This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics. The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics. Contents:Bounded Block Operator Matrices:The Quadratic Numerical RangeSpecial Classes of Block Operator MatricesSpectral InclusionEstimates of the ResolventCorners of the Quadratic Numerical RangeSchur Complements and Their FactorizationBlock DiagonalizationSpectral Supporting SubspacesVariational Principles for Eigenvalues in GapsJ-Self-Adjoint Block Operator MatricesThe Block Numerical RangeNumerical Ranges of Operator PolynomialsGershgorin's Theorem for Block Operator MatricesUnbounded Block Operator Matrices:Relative Boundedness and Relative CompactnessClosedness and Closability of Block Operator MatricesSpectrum and ResolventThe Essential SpectrumSpectral InclusionSymmetric and J-Symmetric Block Operator MatricesDichotomous Block Operator Matrices and Riccati EquationsBlock Diagonalization and Half Range CompletenessUniqueness Results for Solutions of Riccati EquationsVariational PrinciplesEigenvalue EstimatesApplications in Mathematical Physics:Upper Dominant Block Operator Matrices in MagnetohydrodynamicsDiagonally Dominant Block Operator Matrices in Fluid MechanicsOff-Diagonally Dominant Block Operator Matrices in Quantum Mechanics Readership: Mathematicians, physicists and engineers. Keywords:Operator Theory;Spectral Theory;Eigenvalues;Differential Equations;Riccati Equations;Numerical Range;Mathematical Physics;Matrix TheoryKey Features:Challenging spectral problems to which standard methods do not applyNew results even in the finite dimensional caseMany illustrating examplesWide range of possible applicationsReviews:“This book is a valuable addition to the literature and will be of great help for those working in this field already as well as for people looking for an interesting introduction to the topic.”Mathematical Reviews

Invitation To C Algebras And Topological Dynamics

Author: Jun Tomiyama
Publisher: World Scientific
ISBN: 9789971503383
Size: 30.47 MB
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This book is an exposition on the interesting interplay between topological dynamics and the theory of C*-algebras. Researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. This book is designed to present to the readers the subject in an elementary way, including also results of recent developments.

The State Space Method

Author: Daniel Alpay
Publisher: Springer Science & Business Media
ISBN: 9783764373702
Size: 70.66 MB
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The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations. The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists.

Recent Progress In Operator Theory

Author: Israel C. Gohberg
Publisher: Birkhäuser
ISBN: 3034887930
Size: 66.80 MB
Format: PDF
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This volume brings readers up to date on different aspects of operator theory and its applications, including mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and systems. Of practical use to a wide readership in pure and applied mathematics, physics and engineering sciences.