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 weak operator topology
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 topology
to an operator B , then for every A e A and x , y es we have ( BAx , y ) = lim ( BqAx
...
Page 922
topology , i . e . , TnXC → Tx for every x in the space upon which the operators T ,
T1 , T2 , . . . , are defined . 1 LEMMA . Let S , T , Sn , Tm , n 2 1 be bounded linear
operators in Hilbert space with Sn →S , Tn →T in the strong operator topology .
topology , i . e . , TnXC → Tx for every x in the space upon which the operators T ,
T1 , T2 , . . . , are defined . 1 LEMMA . Let S , T , Sn , Tm , n 2 1 be bounded linear
operators in Hilbert space with Sn →S , Tn →T in the strong operator topology .
Page 1921
6 . 16 ( 272 ) complex case , IV . 6 . 17 ( 274 ) remarks on , ( 383 – 385 ) Strictly
convex B - space , definition , VII . 7 ( 458 ) Strictly convex B - space , definition ,
VII . 7 ( 458 ) Strong operator topology , definition , VI . 1 . 2 ( 475 ) properties , VI .
6 . 16 ( 272 ) complex case , IV . 6 . 17 ( 274 ) remarks on , ( 383 – 385 ) Strictly
convex B - space , definition , VII . 7 ( 458 ) Strictly convex B - space , definition ,
VII . 7 ( 458 ) Strong operator topology , definition , VI . 1 . 2 ( 475 ) properties , VI .
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero