Introduction to Linear Operator Theory (Chapman & Hall/CRC Pure and Applied Mathematics) - ISBN:0824768965

Introduction to Linear Operator Theory (Chapman & Hall/CRC Pure and Applied Mathematics)

Date: 02 June 2011, 07:18

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During the last 15 or 20 years much progress has been made in the theory of non-self-adjoint operators on Hilbert and Banach spaces. The present volume is intended to provide an introduction to the subject.
The first four chapters are devoted to standard material on linear functional analysis. However, whenever possible a unified approach is used, and this is the case, for example, for the three basic theorems of linear functional analysis which are treated consequences of a unique theorem. Chapter 5 is concerned with the
general spectral representation of operators on Hilbert spaces and depends on the Banach algebra theory developed in Chapter 4.
Chapter 6 is concerned with the basic notion of this book: the numerical range. First this is considered for Hilbert spaces and next for Banach spaces. Various classes of operators connected with the numerical range are also discussed.
The classes of nonnormal operators have a long history, and the problem of deciding when an operator is normal (also hermitian, unitary) forms the content of Chapters 7 and 8.

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