## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 84

Page 868

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X /

I is isometrically isomorphic to the field of

maximal . PROOF . If I is not maximal it is properly contained in an ideal and so X

/ I ...

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X /

I is isometrically isomorphic to the field of

**complex**numbers if and only if I ismaximal . PROOF . If I is not maximal it is properly contained in an ideal and so X

/ I ...

Page 872

and each x in X define x ( a ) = lim Pn ( a ) where { Pn } is a ... For a fixed do e G

the map x + x ( 20 ) is a homomorphism of X into the field of

**complex**variable that { Pn ( 2 ) } also converges uniformly on G . For each 1 in Gand each x in X define x ( a ) = lim Pn ( a ) where { Pn } is a ... For a fixed do e G

the map x + x ( 20 ) is a homomorphism of X into the field of

**complex**numbers .Page 887

There we associated with an operator T in a

algebra of sets in the

set was defined as any subset of the spectrum o ( T ) which is both open and

closed in ...

There we associated with an operator T in a

**complex**B - space a Booleanalgebra of sets in the

**complex**plane which were called spectral sets . A spectralset was defined as any subset of the spectrum o ( T ) which is both open and

closed in ...

### 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