## 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 |

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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

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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