## Linear Operators: Spectral theory |

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Page 885

It is easily seen that the centralizer No of a B * - algebra A is a B * - algebra . If {

Ba } is a generalized sequence in Ao converging in the

to an operator B , then for every A e A and x , y es we have ( BAx , y ) = lim ( BqAx

...

It is easily seen that the centralizer No of a B * - algebra A is a B * - algebra . If {

Ba } is a generalized sequence in Ao converging in the

**weak**operator topologyto an operator B , then for every A e A and x , y es we have ( BAx , y ) = lim ( BqAx

...

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 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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