## 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 84

Page 1928

Terminology and Preliminary Notions The concepts of a Boolean algebra of

Terminology and Preliminary Notions The concepts of a Boolean algebra of

**projections**, a spectral measure , an integral with respect to a spectral measure , and so on , which have been explained in Section X.1 , are all fundamental for ...Page 2199

If the strongly closed bounded Boolean algebra B of

If the strongly closed bounded Boolean algebra B of

**projections**is not complete , there is , by the preceding lemma , a vector x and an increasing generalized sequence { Ex } of**projections**in B such that the limit lim , Eqx does not ...Page 2218

Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the

Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the

**projections**in its resolution of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of ...### 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