## Linear Operators: General theory |

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Page xiv

Conditions XVII . ... Perturbations of

CHAPTER I Preliminary Concepts The study of linear operations requires xiv

CONTENTS.

**SPECTRAL**THEORY IX . B - Algebras ...**Spectral**Operators : SufficientConditions XVII . ... Perturbations of

**Spectral**Operators with Continuous**Spectra**CHAPTER I Preliminary Concepts The study of linear operations requires xiv

CONTENTS.

Page 574

Let f be in F ( T ) , and let t be a

a neighborhood of t , and let e , ( u ) = 0 for u in a neighborhood of the rest of o ...

Let f be in F ( T ) , and let t be a

**spectral**set of f ( T ) . Then o ( T ) Of - ' ( T ) is a**spectral**set of T , and E ( T ; f ( T ) ) = E ( -1 ( 1 ) ; T ) . Proof . Let e ( u ) = 1 for p ina neighborhood of t , and let e , ( u ) = 0 for u in a neighborhood of the rest of o ...

Page 749

Ann . of Math . ( 2 ) 41 , 639-661 ( 1940 ) . 6.

. 49 , 637-651 ( 1943 ) . 7.

Amer . Math . Soc . 54 , 185–217 ( 1943 ) . 8. Integration and linear operations .

Ann . of Math . ( 2 ) 41 , 639-661 ( 1940 ) . 6.

**Spectral**theo Bull . Amer . Math . Soc. 49 , 637-651 ( 1943 ) . 7.

**Spectral**theory I , Convergence to projections . Trans .Amer . Math . Soc . 54 , 185–217 ( 1943 ) . 8. Integration and linear operations .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero