## 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 2291

Since the notion of an operator with compact

this section , it will be convenient to introduce , in the following definition , a

special term for such operators . 1 DEFINITION . An operator T is discrete if there

is a ...

Since the notion of an operator with compact

**resolvent**occurs so frequently inthis section , it will be convenient to introduce , in the following definition , a

special term for such operators . 1 DEFINITION . An operator T is discrete if there

is a ...

Page 2316

Thus , if Elan ) is to be anything but a projection onto a one - dimensional range ,

it follows from Lemma 2.2 that in must be a multiple pole of the

Lemma 8 , the condition for this is ( on , Yn ) = 0 , where Yin is a solution of ( T * -

In I ...

Thus , if Elan ) is to be anything but a projection onto a one - dimensional range ,

it follows from Lemma 2.2 that in must be a multiple pole of the

**resolvent**. ByLemma 8 , the condition for this is ( on , Yn ) = 0 , where Yin is a solution of ( T * -

In I ...

Page 2363

Then all but a finite number of points in o ( T + P ) are simple poles of the

one of the following conditions holds : ( a ) Mi approaches zero ; ( b ) lim supi- Mi

SK < 0 ...

Then all but a finite number of points in o ( T + P ) are simple poles of the

**resolvent**R ( ) ; T + P ) corresponding to one - dimensional eigenspaces if anyone of the following conditions holds : ( a ) Mi approaches zero ; ( b ) lim supi- Mi

SK < 0 ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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