## 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 91

Page 1913

In Chapter XV we try to stress most of the basic elementary

operators that distinguish them from other operators . These

variety of forms not immediately apparent from the definition of a spectral ...

In Chapter XV we try to stress most of the basic elementary

**properties**of spectraloperators that distinguish them from other operators . These

**properties**assume avariety of forms not immediately apparent from the definition of a spectral ...

Page 2134

Statement of the Problem In the preceding chapter we studied the

bounded spectral operators , that is , operators which have a countably additive

resolution of the identity defined on the field of Borel sets . These operators were

...

Statement of the Problem In the preceding chapter we studied the

**properties**ofbounded spectral operators , that is , operators which have a countably additive

resolution of the identity defined on the field of Borel sets . These operators were

...

Page 2588

3 ( 2265 )

) , XVII . 3 . ... 12 ( 2318 ) 2 - essentially bounded E - measurable functions ,

definition ,

1955 ) ...

3 ( 2265 )

**properties**of , XVII . 3 . 3 ( 2196 ) , XVII. 3 . 4 ( 2197 ) , XVII . 3 . 5 ( 2198) , XVII . 3 . ... 12 ( 2318 ) 2 - essentially bounded E - measurable functions ,

definition ,

**properties**of , XV . 9 ( 1964 ) Eigenvalue , definition of , XV . 8 . 1 (1955 ) ...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

### Other editions - View all

### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero