## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2103

This Wiener theorem and P . Lévy ' s generalization

by any function f ( a ) analytic for d in a neighborhood of the spectrum of the

element a in A , are extensions of the results to be found in IX . 4 . 10 and IX . 4 .

11 .

This Wiener theorem and P . Lévy ' s generalization

**obtained**by replacing 1 / 2by any function f ( a ) analytic for d in a neighborhood of the spectrum of the

element a in A , are extensions of the results to be found in IX . 4 . 10 and IX . 4 .

11 .

Page 2176

He has

analogous theorems . CHAPTER XVII Algebras of Spectral Operators IS 1 .

Introduction 2176 XVI . 8 XVI . SPECTRAL OPERATORS : SUFFICIENT

CONDITIONS.

He has

**obtained**generalizations of the results of this chapter , as well asanalogous theorems . CHAPTER XVII Algebras of Spectral Operators IS 1 .

Introduction 2176 XVI . 8 XVI . SPECTRAL OPERATORS : SUFFICIENT

CONDITIONS.

Page 2405

The same conclusion is readily

to the reader to give the necessary details . Next let Isrs 2 . Let hy be a second

non - negative , u - measurable function defined on S . Then we conclude as

above ...

The same conclusion is readily

**obtained**in the extreme case r = 00 ; we leave itto the reader to give the necessary details . Next let Isrs 2 . Let hy be a second

non - negative , u - measurable function defined on S . Then we conclude as

above ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero