## Linear Operators: Spectral theory |

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Page 885

Proof . It is easily seen that the centralizer Ao of a B * - algebra A is a B * - algebra

. If { Ba } is a generalized sequence in Ao converging in the weak operator

lim ( B ...

Proof . It is easily seen that the centralizer Ao of a B * - algebra A is a B * - algebra

. If { Ba } is a generalized sequence in Ao converging in the weak operator

**topology**to an operator B , then for every AEA and x , y es we have ( BAx , y ) =lim ( B ...

Page 922

, T2 , . . . , are defined . 1 LEMMA . Let S , T , S . , Tn , n 2 1 be bounded linear

operators in Hilbert space with Sn →S , Tn → T in the strong operator

**topology**, i . e . , T , x + Tx for every x in the space upon which the operators T , T1, T2 , . . . , are defined . 1 LEMMA . Let S , T , S . , Tn , n 2 1 be bounded linear

operators in Hilbert space with Sn →S , Tn → T in the strong operator

**topology**.Page 1420

( a ' ) The

sequence in D ( T1 ( T ) ) . Suppose that { { n } converges to zero in the

of D ...

( a ' ) The

**topology**of the Hilbert space D ( Ti ( t ) ) is the same as its relative**topology**as a subspace of the Hilbert space D ( T1 ( + ' ) ) . Indeed , let { In } be asequence in D ( T1 ( T ) ) . Suppose that { { n } converges to zero in the

**topology**of D ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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