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Mathematics - Analysis | Banach Algebra Techniques in Operator Theory

Banach Algebra Techniques in Operator Theory

Series: Graduate Texts in Mathematics, Vol. 179

Douglas, Ronald G.

Originally published by Academic Press in 1972

2nd ed. 1998, XVI, 194 pp.

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Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and mechanics. The intention of this book is to discuss certain advanced topics in operator theory and to provide the necessary background for them assuming only the standard senior-first year graduate courses in general topology, measure theory, and algebra. At the end of each chapter there are source notes which suggest additional reading along with giving some comments on who proved what and when. In addition, following each chapter is a large number of problems of varying difficulty. This new edition will appeal to a new generation of students seeking an introduction to operator theory.

Content Level » Graduate

Keywords » Banach algebra - C*-algebra - Hilbert space - Operator theory - algebra - measure

Related subjects » Analysis

Table of contents 

1 Banach Spaces.- 2 Banach Algebras.- 3 Geometry of Hilbert Space.- 4 Operators on Hilbert Space and C*-Algebras.- 5 Compact Operators, Fredholm Operators, and Index Theory.- 6 The Hardy Spaces.- 7 Toeplitz Operators.- References.

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