## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 66

Page 2017

and the fraction in the

«}«S}1'a which is bounded on all of Rn. Thus As has a resolution of the identity.

Furthermore, the set ®i is the null set {s\a1—32 = 0}, so that As is a scalar type ...

and the fraction in the

**inequality**(i) of Theorem 6 is \sl-3l\2 + 2\Sls2\* {(«!-«!)* + 16«}«S}1'a which is bounded on all of Rn. Thus As has a resolution of the identity.

Furthermore, the set ®i is the null set {s\a1—32 = 0}, so that As is a scalar type ...

Page 2190

Thus for some constant K we have |S(/)| ^ K\f\ and to prove the final

the present theorem it will suffice to prove that |/|B ^ |S(/)| . Since both terms in this

Thus for some constant K we have |S(/)| ^ K\f\ and to prove the final

**inequality**ofthe present theorem it will suffice to prove that |/|B ^ |S(/)| . Since both terms in this

**inequality**are continuous functions of/, it will suffice to prove it for every function/ ...Page 2403

First we shall prove an

elementary in the sense that it relates only to the norms of the integral kernels

involved. We then use this

First we shall prove an

**inequality**for integral operators (Lemma 5 below) which iselementary in the sense that it relates only to the norms of the integral kernels

involved. We then use this

**inequality**to apply Theorem 1 in an illustrative but ...### 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