## 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

2 , each of these finite sums has a finite dimensional range and is hence

, it follows from Lemma V1 . 5 . 3 that for v > 0 the operator ( T - 101 ) - v is

+ do ...

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 - 101 ) - v is

**compact**. Thus , if v > 0 , then since P + T = ( P + 101 ) + ( T - 107 ) , and since ( P+ do ...

Page 2360

It will also be shown that T - v is

, it will follow that B ( u ) = R ( u ; T + P ) is

large , so that the theorem will be proved . Let u be in V . To show that \ T ' ' R ( u ...

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 sufficientlylarge , so that the theorem will be proved . Let u be in V . To show that \ T ' ' R ( u ...

Page 2462

The operator C is

is complete . Q . E . D . 12 LEMMA . If C is a

uniformly bounded sequence of operators in H converging strongly to zero ...

The operator C is

**compact**by Corollary V1 . 5 . 5 , and thus proof of Corollary 11is complete . Q . E . D . 12 LEMMA . If C is a

**compact**operator in H , and { Tn } is auniformly bounded sequence of operators in H converging strongly to zero ...

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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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