## 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 80

Page 2013

For a sequence { om } satisfying ( 3 ) , A is

consists precisely of those o for which the limit in ( 9 ) exists . Our next concern

will be with the question of the existence of a resolution of the identity for A . This

leads ...

For a sequence { om } satisfying ( 3 ) , A is

**given**by ( 9 ) and the domain of Aconsists precisely of those o for which the limit in ( 9 ) exists . Our next concern

will be with the question of the existence of a resolution of the identity for A . This

leads ...

Page 2088

... complex measurable functions on RN and let As be the densely defined closed

operator

operator whose spectrum lies in a left half plane then it is the infinitesimal

generator ...

... complex measurable functions on RN and let As be the densely defined closed

operator

**given**by equations 12 . 4 . Show that if As is a scalar type spectraloperator whose spectrum lies in a left half plane then it is the infinitesimal

generator ...

Page 2096

Another characterization of subscalar operators is

which asserts that , under certain hypotheses , a continuous linear mapping U of

a Banach algebra A with unit e into B ( X ) is the projection of a continuous ...

Another characterization of subscalar operators is

**given**, based on a theoremwhich asserts that , under certain hypotheses , a continuous linear mapping U of

a Banach algebra A with unit e into B ( X ) is the projection of a continuous ...

### 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 | |

47 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 function 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