## 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

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 is maximal . PROOF . If 3 is not maximal it is properly contained in an ...Page 872

**complex**variable that { P ( 2 ) } also converges uniformly on G. For each 1 in G 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 ...Page 887

... 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

... 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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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero