## Linear Operators: General theory |

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Results 1-3 of 63

Page xiv

Conditions XVII . ... Perturbations of

CHAPTER I Preliminary Concepts The study of linear operations requires xiv

CONTENTS.

**SPECTRAL**THEORY IX . B - Algebras X ...**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 | be in F ( T ) , and let t be a

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

...

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

**spectral**set of f ( T ) . Then o ( T ) nf - 1 ( T ) is a**spectral**set of T , and E ( T ; f ( T ) ) = E ( - 1 ( T ) ; T ) . PROOF . Let e ( u ) = 1 for uin a neighborhood of t , and let e , ( u ) = 0 for u in a neighborhood of the rest of o

...

Page 749

( 2 ) 41 , 639 – 661 ( 1940 ) . 6 .

637 - 651 ( 1943 ) . 7 .

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

Trans .

( 2 ) 41 , 639 – 661 ( 1940 ) . 6 .

**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 ) . 8 . Integration and linear operations .

Trans .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect 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