## Linear Operators, Part 2 |

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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

/ 3 ...

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

/ 3 ...

Page 872

and each x in X define x ( a ) = lim Pm ( a ) where { P , } is a sequence of

polynomials with \ P . , ( z ) — « \ + 0 . The number x ( 2 ) is clearly independent of

the ...

**complex**variable that { Po ( 2 ) } also converges uniformly on G . For each 2 in Gand each x in X define x ( a ) = lim Pm ( a ) where { P , } is a sequence of

polynomials with \ P . , ( z ) — « \ + 0 . The number x ( 2 ) is clearly independent of

the ...

Page 1157

Then a

function g which is analytic in a neighborhood of t and is such that g ( x ) = f ( z )

for all z in this neighborhood for which 121 + 1 . Making use of this theorem and ...

Then a

**complex**number t of modulus 1 is outside old ) if and only if there exists afunction g which is analytic in a neighborhood of t and is such that g ( x ) = f ( z )

for all z in this neighborhood for which 121 + 1 . Making use of this theorem and ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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