## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 94

Page 888

where o , d are arbitrary spectral sets and where ® is the void set . ... This

observation leads to the notion of a

...

where o , d are arbitrary spectral sets and where ® is the void set . ... This

observation leads to the notion of a

**spectral measure**in a B - space X . A**spectral****measure**in X is a homomorphic map of a Boolean algebra of sets into a Boolean...

Page 889

5 ) , every set in the domain of a

an open and closed subset of o ( T ) and thus a spectral set . However , in order

to reduce the study of T to its study on invariant subspaces in which it has a

smaller ...

5 ) , every set in the domain of a

**spectral measure**satisfying ( iii ) is necessarilyan open and closed subset of o ( T ) and thus a spectral set . However , in order

to reduce the study of T to its study on invariant subspaces in which it has a

smaller ...

Page 897

It follows then from ( iii ) that the projections E ( d ) also commute with T ( f ) and

this completes the proof of the theorem . Q . E . D . 3 COROLLARY . The

...

It follows then from ( iii ) that the projections E ( d ) also commute with T ( f ) and

this completes the proof of the theorem . Q . E . D . 3 COROLLARY . The

**spectral****measure**is countably additive in the strong operator topology . Proof . If { 8n } is a...

### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

11 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 complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero