## 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 1134

Then , retracing the steps of the above argument , we can conclude that ( I – E )

TE , = 0 for each à in C . Hence T leaves the

, and the set F of projections En , de C , subdiagonalizes T . To prove the second

...

Then , retracing the steps of the above argument , we can conclude that ( I – E )

TE , = 0 for each à in C . Hence T leaves the

**range**of each projection E , invariant, and the set F of projections En , de C , subdiagonalizes T . To prove the second

...

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

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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