## 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

the centralizer 2lc of a S*-algebra 21 is a 2?*-algebra. If {Ba} 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 seen thatthe centralizer 2lc of a S*-algebra 21 is a 2?*-algebra. If {Ba} 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., Tnx -*□ Tx 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**. Then Sn+Tn...

Page 1921

9.1-5 (511), VI.9.11- 12 (512-513) Strong

(419) Structure space of a B-algebra, IX.2.7 (869) Sturm-Liouville operator, XIII.2 (

1291), XIII.9.F (1550) Subadditive function, definition, (618) Subbase for a ...

9.1-5 (511), VI.9.11- 12 (512-513) Strong

**topology**, in a normed space, II.3.1 (59),(419) Structure space of a B-algebra, IX.2.7 (869) Sturm-Liouville operator, XIII.2 (

1291), XIII.9.F (1550) Subadditive function, definition, (618) Subbase for a ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero