## 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 89

Page 2299

Hence we find that for n

j ; T + P ) = B ( u ) . Since Blu ) is clearly the product of the compact operator R ( u

; T ) and a bounded operator , it follows that T + P is a discrete operator .

Hence we find that for n

**sufficiently**large , each u in Cn is in plT + P ) and that R (j ; T + P ) = B ( u ) . Since Blu ) is clearly the product of the compact operator R ( u

; T ) and a bounded operator , it follows that T + P is a discrete operator .

Page 2360

It will be shown below that | T ' ' R ( u ; T ) A S | for u in V , and i

From this it will then follow as above that the function f ( u ) = R ( u ; T + P ) f is

uniformly bounded . It will also be shown that T - v is compact . From this , ( iii ) ,

and ...

It will be shown below that | T ' ' R ( u ; T ) A S | for u in V , and i

**sufficiently**large .From this it will then follow as above that the function f ( u ) = R ( u ; T + P ) f is

uniformly bounded . It will also be shown that T - v is compact . From this , ( iii ) ,

and ...

Page 2394

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,

u ) of the equation to = u o , defined for 0 St < oo and for all

+ , such that oz and os are continuous in t and Me for 0 St < 0 and u

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,

u ) of the equation to = u o , defined for 0 St < oo and for all

**sufficiently**small u e P+ , such that oz and os are continuous in t and Me for 0 St < 0 and u

**sufficiently**...### 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