## Linear Operators: Spectral theory |

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Page 875

It will be

commutative B * - algebra X into the algebra C ( 1 ) of all continuous functions on

the structure space 1 of X is an isometric isomorphism of X onto all of C ( 1 ) .

It will be

**shown**that the homomorphism x + x ( • ) ( see Theorem 2 . 9 ) of acommutative B * - algebra X into the algebra C ( 1 ) of all continuous functions on

the structure space 1 of X is an isometric isomorphism of X onto all of C ( 1 ) .

Page 981

11 , there is a continuous character h on R with H / ( T ( ) ) = f , h ( x ) f ( x ) d « , feL

( R ) . The converse part of Theorem 3 . 11 shows that such a character

determines a homomorphism on A whose restriction to A , is Hj . Thus it has been

11 , there is a continuous character h on R with H / ( T ( ) ) = f , h ( x ) f ( x ) d « , feL

( R ) . The converse part of Theorem 3 . 11 shows that such a character

determines a homomorphism on A whose restriction to A , is Hj . Thus it has been

**shown**...Page 1161

That spectral synthesis is not possible for all functions in Lo was

Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been

on the ...

That spectral synthesis is not possible for all functions in Lo was

**shown**by L .Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been

**shown**by M . Paul Malliavin that spectral synthesis is not possible for all functionson the ...

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### 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