## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 87

Page 2084

Using the fact that the difference R(X; A) — R(X; B) is analytic for A ^ 0, prove that

C is a quasi-nilpotent operator and that R(X;A)=R(\;B) + R(\;C)-j. 55 (McCarthy)

Let T be a spectral operator in a complex

Using the fact that the difference R(X; A) — R(X; B) is analytic for A ^ 0, prove that

C is a quasi-nilpotent operator and that R(X;A)=R(\;B) + R(\;C)-j. 55 (McCarthy)

Let T be a spectral operator in a complex

**B**-**space**X which satisfies the growth ...Page 2351

generalized sort. We begin with a basic definition and with a preliminary

investigation of the concept of adjoints for closed operators in a general .

**B**-**space**X. The present section is devoted to stating and proving results of thisgeneralized sort. We begin with a basic definition and with a preliminary

investigation of the concept of adjoints for closed operators in a general .

**B**-**space**.Page 2484

,a) f+-.

be a Hilbert

**B**||,,0 < oo, where the norm is as specified in Definition 2.13. (c) Show that r+»**B**(8,a) f+-.

**B**(g,g) hm - dor = & \ da T ^-4(«, «)• £_o + -'-oo a — ct i te J-oo a — a Let §be a Hilbert

**space**, and let**B**(9)) be the J?-**space**of all bounded operators in §.### 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