## 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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Results 1-3 of 90

Page 2160

... and this limit is clearly zero . Thus ( 1o I – T ' ) y = 0 . It will next be

the vector x - y is in the closure of the manifold ( 101 – T ' ) X . To see this it will , in

view of Corollary II . 3 . 13 , suffice to show that x * ( x - y ) = 0 for every linear ...

... and this limit is clearly zero . Thus ( 1o I – T ' ) y = 0 . It will next be

**shown**thatthe vector x - y is in the closure of the manifold ( 101 – T ' ) X . To see this it will , in

view of Corollary II . 3 . 13 , suffice to show that x * ( x - y ) = 0 for every linear ...

Page 2226

315 ) has

not be a single functional corresponding to x * ; however , some of the results

presented here can still be generalized . Walsh [ 1 ] showed that if A is a complex

B ...

315 ) has

**shown**that in a complete metrizable locally convex space there maynot be a single functional corresponding to x * ; however , some of the results

presented here can still be generalized . Walsh [ 1 ] showed that if A is a complex

B ...

Page 2360

It will be

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

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 ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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