## Linear Operators: Spectral theory |

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Page 868

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

? 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 /

? 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 { P . } 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 { P . ( 2 ) } also converges uniformly on G . For each 2 in Gand each x in X define x ( a ) = lim Pn ( a ) where { P . } 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 1156

We leave it to the reader to show that the character group of this group is

algebraically and topologically isomorphic with the additive group of real

numbers modulo 2n , or , equivalently , with the multiplicative group of

numbers of unit ...

We leave it to the reader to show that the character group of this group is

algebraically and topologically isomorphic with the additive group of real

numbers modulo 2n , or , equivalently , with the multiplicative group of

**complex**numbers of unit ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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