## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 68

Page 1930

If E is a Boolean algebra of subsets of the

set and the whole plane, in short, if 2 is a field of sets in the

spectral measure E on 2 is called a resolution of the identity (or a spectral ...

If E is a Boolean algebra of subsets of the

**complex plane**which contains the voidset and the whole plane, in short, if 2 is a field of sets in the

**complex plane**, then aspectral measure E on 2 is called a resolution of the identity (or a spectral ...

Page 2084

55 (McCarthy) Let T be a spectral operator in a complex B-space X which

satisfies the growth condition (*) in Theorem XV. 6.7, namely for ... 60 (Bishop)

Let Si denote the Borel subsets of the

valued ...

55 (McCarthy) Let T be a spectral operator in a complex B-space X which

satisfies the growth condition (*) in Theorem XV. 6.7, namely for ... 60 (Bishop)

Let Si denote the Borel subsets of the

**complex plane**C and let T e B(X). A vectorvalued ...

Page 2188

Let Ebea spectral measure in the complex B-space 3E which i3 defined and

countably additive on a a-field E of subsets of a set A and let g be a bounded

Borel measurable function defined on the

gWEtf ...

Let Ebea spectral measure in the complex B-space 3E which i3 defined and

countably additive on a a-field E of subsets of a set A and let g be a bounded

Borel measurable function defined on the

**complex plane**. Then f g(f(A))E(d\) = {gWEtf ...

### 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