## 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 87

Page 2239

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

bounded operator . If x is in E ( 7 ) X as well as in E ( e ) X , it

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

bounded operator . If x is in E ( 7 ) X as well as in E ( e ) X , it

**follows**from the ...Page 2246

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. it

contained in the domain of C . It is clear then that ( XI – C ) R ( 1 ) x = x for x in H ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. it

**follows**that R ( a ) is a bounded operator whose range iscontained in the domain of C . It is clear then that ( XI – C ) R ( 1 ) x = x for x in H ...

Page 2459

Statement ( b ) of our lemma

statement ( a ) of our theorem

dense in Lac ( H ) , it would

. 3 .

Statement ( b ) of our lemma

**follows**at once . If xn e Lac ( H ) and limn ... Thusstatement ( a ) of our theorem

**follows**. If F is a ... If ( il – H ) - Lac ( H ) were notdense in Lac ( H ) , it would

**follow**by the Hahn - Banach theorem ( cf . Corollary II. 3 .

### 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 | |

28 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 contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit 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