## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 58

Page 2125

(P)} and {P(8)* | 8 e £(P)} are total on §. It is proved that every g.s.m. can be

extended to a class D0(P) of Borel subsets of C which is maximal (in a certain

sense) ...

**Borel sets**and if x, y e §, then (P(S)x, y) = +f (P(8k)x, y). (iv) The sets {P(8) | 8 e X>(P)} and {P(8)* | 8 e £(P)} are total on §. It is proved that every g.s.m. can be

extended to a class D0(P) of Borel subsets of C which is maximal (in a certain

sense) ...

Page 2202

It follows from Theorem 2.4 that there is a spectral measure A in X* defined on the

completeness of B, the operator A(e) is, for every

It follows from Theorem 2.4 that there is a spectral measure A in X* defined on the

**Borel sets**in A and such that xT{f)x* ... It will now be shown that, because of thecompleteness of B, the operator A(e) is, for every

**Borel set**e, the adjoint of a ...Page 2233

8 Definition. Let T be a spectral operator with resolution of the identity E, and let /

be a function analytic in an open set U such that E( U) = I. Let {e„} be an arbitrary

increasing sequence of bounded

8 Definition. Let T be a spectral operator with resolution of the identity E, and let /

be a function analytic in an open set U such that E( U) = I. Let {e„} be an arbitrary

increasing sequence of bounded

**Borel sets**with closures contained in U, such ...### 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