## 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 /

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

15 ) will yield , for normal operators in Hilbert space , a reduction theory which is

more complete than that developed in Chapter VII for general operators in a

it ...

15 ) will yield , for normal operators in Hilbert space , a reduction theory which is

more complete than that developed in Chapter VII for general operators in a

**complex**B - space . Although the present chapter is independent of Chapter VII ,it ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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