A Local Spectral Theory for Closed Operators

Ivan N. Erdelyi; Wang Shengwang

doi:10.1017/CBO9780511662249

This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.

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A Local Spectral Theory for Closed Operators

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

PREFACE
pp vii-viii

Glossary of Notations and Symbols
pp ix-x

Chapter I - INTRODUCTION
pp 1-32

Chapter II - THE SPECTRAL DECOMPOSITION PROPERTY
pp 33-60

Chapter III - SPECTRAL DUALITY
pp 61-80

Chapter IV - SPECTRAL RESOLVENTS
pp 81-107

Chapter V - SPECIAL TOPICS IN SPECTRAL DECOMPOSITION
pp 108-147

Appendix A - The (**)-version of the predual theorem
pp 148-160

Appendix B - Some open problems
pp 161-161

BIBLIOGRAPHY
pp 162-176

Index
pp 177-178

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