## Linear Operators: Spectral theory |

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Page 1092

By Lemma 5 and Corollary 4 , and the elementary fact that any compact operator

may be approximated in norm by a sequence of operators Tn with

finitedimensional

T has finite ...

By Lemma 5 and Corollary 4 , and the elementary fact that any compact operator

may be approximated in norm by a sequence of operators Tn with

finitedimensional

**range**, it is enough to prove the lemma in the special case thatT has finite ...

Page 1395

Then ( E ( Q ) U ) x = ( I - E ( { 2 } ) ( 21 – T ) ) x = ( 21 — T ) x which shows that the

V of a which is disjoint from 0 , , and let f ( u ) = ( 2 - - u ) - 1 if u € V and f ( u ) = 0 ...

Then ( E ( Q ) U ) x = ( I - E ( { 2 } ) ( 21 – T ) ) x = ( 21 — T ) x which shows that the

**range**of the projection E ( 01 ) contains the**range**of T . Choose a neighborhoodV of a which is disjoint from 0 , , and let f ( u ) = ( 2 - - u ) - 1 if u € V and f ( u ) = 0 ...

Page 1397

This readily yields a contradiction as follows : the assumption that 0 0 ( T ) implies

that the

seen to be symmetric — obtained by restricting T * to D ( T ) + N . Then the

R ...

This readily yields a contradiction as follows : the assumption that 0 0 ( T ) implies

that the

**range**R ( T ) of T is closed . Let T be the extension — which is easilyseen to be symmetric — obtained by restricting T * to D ( T ) + N . Then the

**range**R ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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