## Linear Operators: Spectral operators |

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Page 1947

Let B , ... , Bx be a finite collection of commuting

projections in a Hilbert space H. Then there exists a

operator B in H with a

a self ...

Let B , ... , Bx be a finite collection of commuting

**bounded**Boolean algebras ofprojections in a Hilbert space H. Then there exists a

**bounded**self adjointoperator B in H with a

**bounded**everywhere defined inverse such that BEB - 1 isa self ...

Page 2169

uniform limit of analytic functions , it follows that this map is also a homomorphism

on the algebra of continuous functions . To see that it is a homomorphism on the

algebra of

uniform limit of analytic functions , it follows that this map is also a homomorphism

on the algebra of continuous functions . To see that it is a homomorphism on the

algebra of

**bounded**Borel functions , note that for a fixed continuous function g ...Page 2239

Since f Xe is a

If x is in E ( ē ) X as well as in E ( e ) X , it follows from the operational calculus for

Since f Xe is a

**bounded**function , the operator T ' ( f Xe ) is a**bounded**operator .If x is in E ( ē ) X as well as in E ( e ) X , it follows from the operational calculus for

**bounded**functions ( cf. XVII.2.10 ) that T ( fXe ) x = T ( fxe ) E ( 7 ) x = T ( fXeč ) x ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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