## Linear Operators: General theory |

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**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 ) nf- ( ) is a**spectral**set of T , and E ( t ; f ( T ) ) E ( -1 ( T ) ; T ) . Proof . Let e ( u ) = 1 for u in a neighborhood of t , and let eq ( u ) = 0 for u in ...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 ) . 8. Integration and linear operations . Trans . Amer . Math .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero