## Linear Operators: Spectral theory |

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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 weak operator

that the centralizer A of a B * -algebra A is a B * -algebra . If { Br } is a generalized

...

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

operators and is closed in the weak operator

**topology**. Proof . It is easily seenthat the centralizer A of a B * -algebra A is a B * -algebra . If { Br } is a generalized

...

Page 922

T2 , ... , are defined . 1 LEMMA . Let S , T , Sn , 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 → Tr for every x in the space upon which the operators T , T1 ,T2 , ... , are defined . 1 LEMMA . Let S , T , Sn , Tn , n 2 1 be bounded linear

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

**topology**.Page 1921

... Liouville operator , XIII.2 ( 1291 ) , XIII.9.F ( 1550 ) Subadditive function ,

definition , ( 618 ) Subbase for a

Subspace , of a linear space , ( 36 ) . ( See also Manifold ) Summability , of

Fourier series ...

... Liouville operator , XIII.2 ( 1291 ) , XIII.9.F ( 1550 ) Subadditive function ,

definition , ( 618 ) Subbase for a

**topology**, 1.4.6 ( 10 ) criterion for , 1.4.8 ( 11 )Subspace , of a linear space , ( 36 ) . ( See also Manifold ) Summability , of

Fourier series ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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 complete 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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero