## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 23

Page 868

two - sided and the quotient algebra X / I is again a

be a B - algebra if I is closed ( 1 . 13 ) . It is readily seen that every ideal I in X ...

**Commutative**B - Algebras In case X is a**commutative**B - algebra every ideal I istwo - sided and the quotient algebra X / I is again a

**commutative**algebra . It willbe a B - algebra if I is closed ( 1 . 13 ) . It is readily seen that every ideal I in X ...

Page 869

Every homomorphism of a

system is continuous . 4 LEMMA . Let M be the set of maximal ideals in the

" .

Every homomorphism of a

**commutative**B - algebra into the complex numbersystem is continuous . 4 LEMMA . Let M be the set of maximal ideals in the

**commutative**B - algebra X . Then æ ( M ) = 0 ( x ) and sup \ X ( M ) ] = lim ( x " | 1 /" .

Page 882

Nelson Dunford, Jacob T. Schwartz. where E is an arbitrary Borel subset of R ,

and E , = { ( x , y ) e RXR 100 + ye E } . Show that with the product u * 2 the

Banach space M is a

if 2 ( E ) ...

Nelson Dunford, Jacob T. Schwartz. where E is an arbitrary Borel subset of R ,

and E , = { ( x , y ) e RXR 100 + ye E } . Show that with the product u * 2 the

Banach space M is a

**commutative**Banach algebra . 14 If f is in L / ( - 0 , 00 ) , andif 2 ( E ) ...

### What people are saying - Write a review

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

### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero