## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 59

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

that the centralizer Qs" of a B"-algebra Qs 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 Qs is a B"-algebra. If {B,} is a generalized ...

Page 922

topology, i.e., T., a -> Tr for every a 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

topology, i.e., T., a -> Tr for every a 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.--To ...Page 1921

(See

, (419) study of, I.6 norm or strong, in a ... I.4–8 weak, in a B-space, (419) weak*

topology, (462) 3 and £" topologies in 3:*, (419) Total boundedness, in a metric ...

(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 weak, in a B-space, (419) weak*

topology, (462) 3 and £" topologies in 3:*, (419) Total boundedness, in a metric ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic applied 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 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 measure multiplicity 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