## 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 3 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 3 is not maximal it is properly contained in an ideal and so X

/ I ...

Page 872

and each x in X define x ( 2 ) = lim P ( 2 ) where { Pn } is a sequence of

polynomials with Pņ ( 2 ) -x +0 . The number x ( 2 ) is clearly independent of the

particular ...

**complex**variable that { P ( 2 ) } also converges uniformly on G. For each 1 in Gand each x in X define x ( 2 ) = lim P ( 2 ) where { Pn } is a sequence of

polynomials with Pņ ( 2 ) -x +0 . The number x ( 2 ) is clearly independent of the

particular ...

Page 887

... The spectral theorem to be proved in this chapter will introduce a theory which

parallels in Hilbert space the theory in n - dimensional unitary space associated

with the classical reduction of a finite normal matrix of

... The spectral theorem to be proved in this chapter will introduce a theory which

parallels in Hilbert space the theory in n - dimensional unitary space associated

with the classical reduction of a finite normal matrix of

**complex**numbers .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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