## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 89

Page 2169

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

on the algebra of

algebra of bounded Borel functions, note that for a fixed

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 thealgebra of bounded Borel functions, note that for a fixed

**continuous function**g ...Page 2456

We therefore find that equation (4) is valid whenever F is a

vanishing outside a compact subset of the ... 6, it follows that we can find a

sequence Fn of

of the ...

We therefore find that equation (4) is valid whenever F is a

**continuous function**vanishing outside a compact subset of the ... 6, it follows that we can find a

sequence Fn of

**continuous functions**, each vanishing outside a compact subsetof the ...

Page 2488

(Hint: Consider A self adjoint, and expand in the eigenvectors of A.) 17 (a) Let /

be a

denote its total variation. Show that el'f(x) dx ^ 2 max |/(*)| + V(f). sa<b (Hint:

Integrate ...

(Hint: Consider A self adjoint, and expand in the eigenvectors of A.) 17 (a) Let /

be a

**continuous function**of bounded variation on an interval [a, b], and let V{f)denote its total variation. Show that el'f(x) dx ^ 2 max |/(*)| + V(f). sa<b (Hint:

Integrate ...

### 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 bounded spectral commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote differential operator disjoint Doklady Akad domain eigenvalues elements equation equivalent exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial preceding 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