## Linear Operators: Spectral operators |

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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 Qs" of a B+-algebra QI is a B"-algebra. If {B,} 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 Qs" of a B+-algebra QI is a B"-algebra. If {B,} is a generalized ...

Page 922

T2, ..., are defined. 1 LEMMA. Let S, T, S, , T., n > 1 be bounded linear operators

in Hilbert space with S, -> S, T, -> T in the strong operator

**topology**, i.e., T., a -> Tr for every r in the space upon which the operators T, T1,T2, ..., are defined. 1 LEMMA. Let S, T, S, , T., n > 1 be bounded linear operators

in Hilbert space with S, -> S, T, -> T in the strong operator

**topology**. Then S,--T ...Page 1921

(See Operator

, (419) study of, I.6 norm or strong, in a ... I.4–8

(49)

(See Operator

**topology**) metric, definition, I.6.1 (18) metric or strong, in a B-space, (419) study of, I.6 norm or strong, in a ... I.4–8

**topological**group, definition, II.1.1(49)

**topological**space, definition, I.4.1 (10) study of, I.4–8 weak, in a B-space, ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero