Title Spectral theory of block operator matrices and applications / Christiane Tretter

Published London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., ©2008

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Description 1 online resource (xxxii, 264 pages) : color illustrations Contents 1. Bounded Block Operator Matrices -- Quadratic Numerical Range -- Special Classes of Block Operator Matrices -- Spectral Inclusion -- Estimates of the Resolvent -- Corners of the Quadratic Numerical Range -- Schur Complements and Their Factorization -- Block Diagonalization -- Spectral Supporting Subspaces -- Variational Principles for Eigenvalues in Gaps -- J-Self-Adjoint Block Operator Matrices -- Block Numerical Range -- Numerical Ranges of Operator Polynomials -- Gershgorin's Theorem for Block Operator Matrices -- 2. Unbounded Block Operator Matrices -- Relative Boundedness and Relative Compactness -- Closedness and Closability of Block Operator Matrices -- Spectrum and Resolvent -- Essential Spectrum -- Spectral Inclusion -- Symmetric and J-Symmetric Block Operator Matrices -- Dichotomous Block Operator Matrices and Riccati Equations -- Block Diagonalization and Half Range Completeness -- Uniqueness Results for Solutions of Riccati Equations -- Variational Principles -- Eigenvalue Estimates -- 3. Applications in Mathematical Physics -- Upper Dominant Block Operator Matrices in Magnetohydrodynamics -- Diagonally Dominant Block Operator Matrices in Fluid Mechanics -- Off-Diagonally Dominant Block Operator Matrices in Quantum Mechanics Summary "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: nonselfadjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics."--Back cover Bibliography Includes bibliographical references (pages 239-260) and index Notes Print version record Subject Operator theory. Matrices. Spectral theory (Mathematics) MATHEMATICS -- Functional Analysis. Matrices Operator theory Spectral theory (Mathematics) Operatormatrix Form Electronic book ISBN 9781848161122 1848161123

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