## Linear Operators, Part 2 |

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Page 885

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

operators and

that the centralizer '2I° of a B*-algebra 91

...

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

**is**a B*-algebra ofoperators and

**is**closed in the weak operator topology. Paoor. It**is**easily seenthat the centralizer '2I° of a B*-algebra 91

**is**a B"'-algebra. If {**Ba**}**is**a generalized...

Page 1343

for 1 E e,,— U23 e,, it

and (b) of the lemma for all /l in the set ... if eo

10

...

for 1 E e,,— U23 e,, it

**is**clear that functions an and (pi satisfy the requirements (a)and (b) of the lemma for all /l in the set ... if eo

**is**any compact subset of**ba**, and10

**is**any point of eo, then there**is**a neighborhood of 1° in eo in which there exist...

Page 1885

... (1668) A(D) (2-12) Á(11) (601) A' (I) (1280) A(T, n) (661) A('(I) (242) AP (242) /T

(11)

) B(S, 2) (240) BV(I) (241) B(I. D) (61) c (239) eu (939) cø(S. E) (240) oa(S. Z, ...

... (1668) A(D) (2-12) Á(11) (601) A' (I) (1280) A(T, n) (661) A('(I) (242) AP (242) /T

(11)

**ba**(**S**. 2) (240)**ba**(**S**. Z, I) (160) ba (240) bu (239) bw (939) (B (895) B(S) (240) B(S, 2) (240) BV(I) (241) B(I. D) (61) c (239) eu (939) cø(S. E) (240) oa(S. Z, ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

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 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 f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero