## Linear Operators, Part 2 |

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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 T , 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 T , with

finitedimensional

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

Page 1134

Nelson Dunford, Jacob T. Schwartz. described in the hypotheses of the present

theorem . Then , retracing the steps of the above argument , we can conclude that

( I – Eq ) TE , = 0 for each 2 in C . Hence T leaves the

Nelson Dunford, Jacob T. Schwartz. described in the hypotheses of the present

theorem . Then , retracing the steps of the above argument , we can conclude that

( I – Eq ) TE , = 0 for each 2 in C . Hence T leaves the

**range**of each projection E ...Page 1395

Then ( E ( 0 ) U ) x = ( 1 - E ( { A } ) ( 21 – T ) ) x = ( 11 — T ) x which shows that the

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

Then ( E ( 0 ) U ) x = ( 1 - E ( { A } ) ( 21 – T ) ) x = ( 11 — T ) x which shows that the

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

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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