## Linear Operators, Part 2 |

### From inside the book

Results 1-3 of 55

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 '2I° of a B*-algebra 91 is a B"'-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**. Paoor. It is easily seenthat the centralizer '2I° of a B*-algebra 91 is a B"'-algebra. If {Ba} is a generalized

...

Page 922

topology, i.e., Tam -> Ta: for every .2: in the space upon which the operators T, T1

, T2, . . ., are defined. 1 LEMMA. Let S, T, S", Tn, n g 1 be bounded linear

operators in Hilbert space with Sn —> S, Tn —> T in the strong

topology, i.e., Tam -> Ta: for every .2: in the space upon which the operators T, T1

, T2, . . ., are defined. 1 LEMMA. Let S, T, S", Tn, n g 1 be bounded linear

operators in Hilbert space with Sn —> S, Tn —> T in the strong

**operator topology**.Page 1921

... (883-385) Strictly convex B-space, definition, V11.7 (458) Strictly convex B-

space, definition, \'1l.7 (458) Strong

properties, V1.9.1~5 (511), V1.9.11I2 (512-518) Strong topology, in a normed

space, ...

... (883-385) Strictly convex B-space, definition, V11.7 (458) Strictly convex B-

space, definition, \'1l.7 (458) Strong

**operator topology**, definition, v1.1.2 (475)properties, V1.9.1~5 (511), V1.9.11I2 (512-518) Strong topology, in a normed

space, ...

### 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 | |

13 other sections not shown

### Other editions - View all

### 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