## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 75

Page 1947

Let S1; . . . , SBk 6e a finite collection of

projections in a Hilbert space §. Then there exists a bounded self adjoint operator

B in § with a bounded everywhere defined inverse such that BEB'1 is a self ...

Let S1; . . . , SBk 6e a finite collection of

**commuting**bounded Boolean algebras ofprojections in a Hilbert space §. Then there exists a bounded self adjoint operator

B in § with a bounded everywhere defined inverse such that BEB'1 is a self ...

Page 1948

The sum and the product of two

space are also spectral operators. The proof of this corollary will use the following

lemma. 6 Lemma. Let A and B be bounded operators in Hilbert space with A ...

The sum and the product of two

**commuting**bounded spectral operators in Hilbertspace are also spectral operators. The proof of this corollary will use the following

lemma. 6 Lemma. Let A and B be bounded operators in Hilbert space with A ...

Page 2177

Introduction The sum and product of two

in Hilbert space is normal and hence spectral. In Corollary XV. 6.5 it was seen

that this principle could be extended to the sum and product of two

Introduction The sum and product of two

**commuting**bounded normal operatorsin Hilbert space is normal and hence spectral. In Corollary XV. 6.5 it was seen

that this principle could be extended to the sum and product of two

**commuting**...### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero