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Page xiv
SPECTRAL THEORY IX . ... Spectral Operators : Sufficient Conditions XVII . ... Perturbations of Spectral Operators with Continuous Spectra CHAPTER I Preliminary Concepts The study of linear operations requires xiv CONTENTS.
SPECTRAL THEORY IX . ... Spectral Operators : Sufficient Conditions 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 spectral set of f ( T ) . Then o ( T ) Of - ' ( T ) is a spectral set of T , and E ( T ; f ( T ) ) = E ( - ( ) ; T ) . Proof . Let e ( u ) = 1 for u in a neighborhood of t , and let e ( u ) = 0 for u ...
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 ( - ( ) ; T ) . Proof . Let e ( u ) = 1 for u in a neighborhood of t , and let e ( u ) = 0 for u ...
Page 749
Spectral theory . Bull . Amer . Math . Soc . 49 , 637-651 ( 1943 ) . 7. Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185–217 ( 1943 ) . Integration and linear operations . Trans . Amer . Math . Soc .
Spectral theory . Bull . Amer . Math . Soc . 49 , 637-651 ( 1943 ) . 7. Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185–217 ( 1943 ) . Integration and linear operations . Trans . Amer . Math . Soc .
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero