## 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 2357

Since , by Lemma 2.2 , each of these finite sums has a finite dimensional range and is hence

Since , by Lemma 2.2 , each of these finite sums has a finite dimensional range and is hence

**compact**, it follows from Lemma V1.5.3 that for v > 0 the operator ( T - 001 ) - " is**compact**. Thus , if v > 0 , then since P + T = ( P + do I ) ...Page 2360

It will also be shown that T - v is

It will also be shown that T - v is

**compact**. From this , ( iii ) , and Theorem VI.5.4 , it will follow that B ( u ) = R ( u ; T + P ) is**compact**for u in V , and i sufficiently large , so that the theorem will be proved .Page 2462

is

is

**compact**. Put C = QR4 , and D = R2 , so that V = CD . The operator C is**compact**by Corollary V1.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a**compact**operator in H , and { Tn } is a uniformly bounded ...### What people are saying - Write a review

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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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