## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 68

Page 898

The uniquely defined spectral measure associated , in Corollary 4 , with the

normal operator T is called the

this notion of the

...

The uniquely defined spectral measure associated , in Corollary 4 , with the

normal operator T is called the

**resolution**of the identity for T. In order to relatethis notion of the

**resolution**of the identity with that given in Section 1 we state the...

Page 920

Let E and Ě be the

Corollary 2.7 it is ... A Formula for the Spectral

operators it is important to have a method for calculating the

identity .

Let E and Ě be the

**resolutions**of the identity for T and † respectively . FromCorollary 2.7 it is ... A Formula for the Spectral

**Resolution**In working with specificoperators it is important to have a method for calculating the

**resolution**of theidentity .

Page 1128

( b ) Every projection in the spectral

combinations of the projections E ;. This we do as follows . Let A be the

commutative B * -algebra of operators generated by the projections E ; and let /

be its spectrum ...

( b ) Every projection in the spectral

**resolution**of T is the strong limit of linearcombinations of the projections E ;. This we do as follows . Let A be the

commutative B * -algebra of operators generated by the projections E ; and let /

be its spectrum ...

### What people are saying - Write a review

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

### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

57 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero