Approximation of Additive Convolution-Like Operators Real C*-Algebra
Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional
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Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta, USA) Benoît Perthame (Ecole Normale Supérieure, Paris, France) Laurent Saloff-Coste (Cornell University, Rhodes Hall, USA) Igor Shparlinski (Macquarie University, New South Wales, Australia) Wolfgang Sprössig (TU Bergakademie, Freiberg, Germany) Cédric Villani (Ecole Normale Supérieure, Lyon, France)
Victor D. Didenko Bernd Silbermann
Approximation
of
Additive
Convolution-Like
Operators Real C*-Algebra Approach
Birkhäuser Verlag Basel . Boston . Berlin
Authors: Victor D. Didenko Department of Mathematics University of Brunei Darussalam Gadong BE 1410 Brunei e-mail: [email protected] [email protected]
Bernd Silbermann Fakultät für Mathematik TU Chemnitz 09107 Chemnitz Germany e-mail: [email protected]
2000 Mathematical Subject Classification: 31-xx, 35-xx,45-xx, 46-xx, 47-xx, 65-xx, 74-xx, 76-xx, 76-xx. In particular: 31A10, 31A30, 35Q15, 35Q30, 45A05, 45B05, 45Exx, 45L05, 45P05, 46N20, 46N40, 47B35, 47Gxx, 47N40, 65E05, 65Jxx, 65R20, 74B10, 74G15, 74Kxx, 74S15, 76D05
Library of Congress Control Number: 2008925217
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 978-3-7643-8750-1 Birkhäuser Verlag AG, Basel · Boston · Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8750-1
e-ISBN 978-3-7643-8751-8
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Contents Preface
ix
1 Complex and Real Algebras 1.1 Complex and Real C ∗ -Algebras . . . . . . . . . . . . . . . . . . . . 1.2 Real Extensions of Complex ∗ -Algebras . . . . . . . . . . . . . . . 1.3 Uniqueness of Involution in Real Extensions of Complex ∗ -Algebras 1.4 Real and Complex Spectrum. Inverse Closedness . . . . . . . . . . 1.5 Moore-Penrose Invertibility in Algebra A˜ . . . . . . . . . . . . . . 1.6 Operator Sequences: Stability . . . . . . . . . . . . . . . . . . . . . 1.7 Asymptotic Moore-Penrose Invertibility . . . . . . . . . . . . . . . 1.8 Approximation Methods in Para-Algebras . . . . . . . . . . . . . . 1.9 Local Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9.1 Gohberg-Krupnik Local Principle . . . . . . . . . . . . . . . 1.9.2 Allan’s Local Principle . . . . . . . . . . . . . . . . . . . . 1.9.3 Local Principle for Para-algebras . . . . . . . . . . . . . . . 1.10 Singular Integral and Mellin Op
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