## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 82

Page 2244

Let S be a set, E a a-field of subsets of S, and E a strongly countably additive

resolution of the identity defined on E.

on S. Then the operator T(f) of Definition 10 is a scalar type spectral operator,

whose ...

Let S be a set, E a a-field of subsets of S, and E a strongly countably additive

resolution of the identity defined on E.

**Let f**be a E-measurable function definedon S. Then the operator T(f) of Definition 10 is a scalar type spectral operator,

whose ...

Page 2424

Let 9ybea Hilhert space, and let B(9y) be the B-space of all bounded operators in

§. Let y and /3 be two real numbers, with y > 0 and 1>j8>0. Let A e <Hy_B{B{9y)),

and

Let 9ybea Hilhert space, and let B(9y) be the B-space of all bounded operators in

§. Let y and /3 be two real numbers, with y > 0 and 1>j8>0. Let A e <Hy_B{B{9y)),

and

**let f**be an infinitely differentiable ^-valued function of a real variable which ...Page 2488

(e) Prove that if A is an operator of the Hilbert-Schmidt class, while w e Łac (//)

and \\w\\H < oo, then

, and expand in the eigenvectors of A.) 17 (a)

(e) Prove that if A is an operator of the Hilbert-Schmidt class, while w e Łac (//)

and \\w\\H < oo, then

**f**+ "\AeitHw\2 dtŁ2ir \\A |j| |M& . (Hint: Consider .4 self adjoint, and expand in the eigenvectors of A.) 17 (a)

**Let**/ be a continuous function of ...### 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