## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 74

Page 2116

then the function 8 defined for F e & by S{F) = E(F)X yields a spectral capacity. ...

Similarly, the operational calculus of

operator was developed in Dunford [17]; in a sense spectral operators were

introduced ...

then the function 8 defined for F e & by S{F) = E(F)X yields a spectral capacity. ...

Similarly, the operational calculus of

**bounded Borel functions**of a spectraloperator was developed in Dunford [17]; in a sense spectral operators were

introduced ...

Page 2169

uniform limit of analytic functions, it follows that this map is also a homomorphism

on the algebra of continuous functions. To see that it is a homomorphism on the

algebra of

uniform limit of analytic functions, it follows that this map is also a homomorphism

on the algebra of continuous functions. To see that it is a homomorphism on the

algebra of

**bounded Borel functions**, note that for a fixed continuous function g ...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

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