## 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

If H ( T ( f ) ) does not vanish identically for f in Li ( R ) then , as was

first part of the proof of Theorem 3 . 11 , there is a continuous character h on R

with H ( T ( 1 ) ) = Jah ( x ) f ( x ) dx , feL ( R ) . The converse part of Theorem 3 .

If H ( T ( f ) ) does not vanish identically for f in Li ( R ) then , as was

**shown**in thefirst part of the proof of Theorem 3 . 11 , there is a continuous character h on R

with H ( T ( 1 ) ) = Jah ( x ) f ( x ) dx , feL ( R ) . The converse part of Theorem 3 .

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

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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