## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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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 { Pņ ( 2 ) } also converges uniformly on G. For each 1 in G and each x in X define x ( a ) = lim P ( 2 ) where { P , } is a sequence of polynomials with P , ( z ) - x + 0. The number x ( ) is clearly independent of ...Page 1157

k = 1 Then a

k = 1 Then a

**complex**number t of modulus 1 is outside o ( d ) if and only if there erists a function g which is analytic in a neighborhood of t and is such that g ( z ) = | ( 2 ) for all z in this neighborhood for which [ 2 ] # 1 .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero