## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Results 1-3 of 78

Page 2357

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

and is hence

- 001 ) - " is

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 ) + ( T - 001 ) ...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 M be in V :. To show that \ T''R ( u ;

T ) ...

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 M be in V :. To show that \ T''R ( u ;

T ) ...

Page 2462

The operator C is

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

uniformly bounded sequence of operators in H converging strongly to zero , then

...

The operator C is

**compact**by Corollary V1.5.5 , and thus proof of Corollary 11 iscomplete . 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 , then

...

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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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