## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 63

Page 889

5 ) , every set in the domain of a spectral measure satisfying ( iii ) is necessarily

an open and closed subset of o ( T ) and ... a spectral measure which is defined

on the Boolean algebra B of all

for ...

5 ) , every set in the domain of a spectral measure satisfying ( iii ) is necessarily

an open and closed subset of o ( T ) and ... a spectral measure which is defined

on the Boolean algebra B of all

**Borel sets**in the plane and which satisfies ( iv )for ...

Page 913

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

0 , and such that if e is a Borel subset of the complement en of en and No v ; ( e )

...

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

**Borel set**e . ... 14 ) , let { en } be a sequence of**Borel sets**such that X = v ; ( en ) =0 , and such that if e is a Borel subset of the complement en of en and No v ; ( e )

...

Page 1218

Let u be a finite positive regular measure on the

R . Then , for every B - space valued u - measurable function f on R and every e >

0 there is a

Let u be a finite positive regular measure on the

**Borel sets**of a topological spaceR . Then , for every B - space valued u - measurable function f on R and every e >

0 there is a

**Borel set**o in R with u ( o ) < ε and such that the restriction of f to ...### 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