## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

### From inside the book

Results 1-3 of 79

Page 2070

In view of ( 14 ) the linear set L , is a B - space under the

In view of ( 14 ) the linear set L , is a B - space under the

**norm**( 16 ) Iflo = \ f11 + llfll , felo , where | f || is the**norm**in X. We let A , consist of all operators in H which have the form ( 17 ) a = ae + f , fe L. Theorem 1 ...Page 2450

Let A be the set of all operators A € B ( X ) for which AX & D ( R ) and for which RA belongs to the HilbertSchmidt class HS , and let ||| A || || RA || , so that the

Let A be the set of all operators A € B ( X ) for which AX & D ( R ) and for which RA belongs to the HilbertSchmidt class HS , and let ||| A || || RA || , so that the

**norm**of an element A ¢ A is simply the Hilbert - Schmidt**norm**of the ...Page 2462

Moreover , if C belongs to the trace class 61 , then TnC converges to zero in trace

Moreover , if C belongs to the trace class 61 , then TnC converges to zero in trace

**norm**, and CT * converges to zero in trace**norm**. PROOF . The set K = C ( { Xe H || 2 < 1 } ) is conditionally compact , and thus for each ε > there ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero