## 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

Since the notion of an operator with compact

**resolvent**occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . 1 DEFINITION .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

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**. By Lemma 8 , the condition for this is ( on , Yn ) = 0 , where Yin is a ...Page 2363

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

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 any one of the following conditions holds : ( a ) Mi approaches zero ; ( b ) lim ...### What people are saying - Write a review

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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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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 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