## Linear Operators: General theory |

### From inside the book

Results 1-3 of 67

Page xiv

**SPECTRAL**THEORY IX . B - Algebras X. Bounded Normal Operators in Hilbert Space XI . Various Special Classes of Operators in L , XII . Unbounded Operators in Hilbert Space XIII . Ordinary Differential Operators XIV .Page 574

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

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 .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero