## Linear Operators, Part 2 |

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Page 885

The centralizer of a B * - algebra of operators in Hilbert space is a B * - algebra of

operators and is closed in the

converging in the

The centralizer of a B * - algebra of operators in Hilbert space is a B * - algebra of

operators and is closed in the

**weak**... If { B } is a generalized sequence in Xoconverging in the

**weak**operator topology to an operator B , then for every A EA ...Page 1919

15 Sequential compactness , definition , 1 . 6 . 10 ( 21 ) relations with other

compactness in metric spaces , 1 . 6 . 13 ( 21 ) , 1 . 6 . 15 ( 22 )

II . 3 . 25 ( 67 ) in reflexive spaces , II . 3 . 28 ( 68 ) in special spaces , IV . 15

Series .

15 Sequential compactness , definition , 1 . 6 . 10 ( 21 ) relations with other

compactness in metric spaces , 1 . 6 . 13 ( 21 ) , 1 . 6 . 15 ( 22 )

**weak**, definition ,II . 3 . 25 ( 67 ) in reflexive spaces , II . 3 . 28 ( 68 ) in special spaces , IV . 15

Series .

Page 1923

10 . 9 ( 325 ) covering theorem , III . 12 . 2 ( 212 ) W

criteria for in special spaces , IV . 15 definition , II . 3 . 25 ( 67 )

completeness , definition , II . 3 . 25 ( 67 ) equivalence of

convergence in L , IV .

10 . 9 ( 325 ) covering theorem , III . 12 . 2 ( 212 ) W

**Weak**Cauchy sequence ,criteria for in special spaces , IV . 15 definition , II . 3 . 25 ( 67 )

**Weak**completeness , definition , II . 3 . 25 ( 67 ) equivalence of

**weak**and strongconvergence in L , IV .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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 derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function give 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