## Linear Operators: Spectral operators |

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If E is a Boolean algebra of subsets of the complex plane which contains the void

set and the whole plane, in short, if E is

a spectral measure E on E is called a resolution of the identity (or a spectral ...

If E is a Boolean algebra of subsets of the complex plane which contains the void

set and the whole plane, in short, if E is

**a field**of sets in the complex plane, thena spectral measure E on E is called a resolution of the identity (or a spectral ...

Page 2143

11 Theorem (A, B). Let Tbea bounded linear operator in the complex B -space X.

Then there is a unique spectral measure on

This spectral measure is bounded, is countably additive on £f(T), and commutes

...

11 Theorem (A, B). Let Tbea bounded linear operator in the complex B -space X.

Then there is a unique spectral measure on

**the field**S?(T) with the propertiesThis spectral measure is bounded, is countably additive on £f(T), and commutes

...

Page 2145

First of all the spectral measure E is not necessarily a resolution of the identity for

T, for, even though it commutes with T, it may not satisfy the inclusion relation cr(

T6) £ 8 (cf. Definition XV. 2. 2, or Definition 1 below). Second,

First of all the spectral measure E is not necessarily a resolution of the identity for

T, for, even though it commutes with T, it may not satisfy the inclusion relation cr(

T6) £ 8 (cf. Definition XV. 2. 2, or Definition 1 below). Second,

**the field**£f(T) or ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator Akad Amer analytic applications arbitrary assume B-space Banach space belongs Boolean algebra Borel sets bounded bounded operator Chapter clear closed commuting compact complex consider constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity Nauk norm normal perturbation plane positive preceding present problem projections Proof properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero