## 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 72

Page 1909

The exclusion of the theory of spectral operators from Part II was not due solely to the growth of the literature in this field , but was determined also by our desire to

The exclusion of the theory of spectral operators from Part II was not due solely to the growth of the literature in this field , but was determined also by our desire to

**present**a number of important applications of the general theory ...Page 2058

In explaining these implications in nonmathematical terms he envisaged , in his Philosophical Essay on Probabilities ( 1814 ) , a kind of superhuman calculator who could , upon having complete knowledge of the

In explaining these implications in nonmathematical terms he envisaged , in his Philosophical Essay on Probabilities ( 1814 ) , a kind of superhuman calculator who could , upon having complete knowledge of the

**present**state of the ...Page 2227

The

The

**present**chapter is an attempt to make the corresponding step in the theory of spectral operators . We begin by defining a closed spectral operator and its resolution of the identity , and showing that the latter is unique .### 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