## 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 /

has ...

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 /

has ...

Page 872

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

polynomials with [ Pn ( 2 ) — x | = 0 . The number x ( 2 ) is clearly independent of

the ...

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

polynomials with [ Pn ( 2 ) — x | = 0 . The number x ( 2 ) is clearly independent of

the ...

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 | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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