## 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 1951

Q . E . D 3

E ( 0 ) with 0 € 7 . PROOF . By

closed twosided ideal in B ( x ) and so the present

D ...

Q . E . D 3

**COROLLARY**. If T is compact , then so are S , N , and every projectionE ( 0 ) with 0 € 7 . PROOF . By

**Corollary**VI . 5 . 5 the compact operators form aclosed twosided ideal in B ( x ) and so the present

**corollary**is immediate . Q . E .D ...

Page 1952

6

0 if 0 € 7 ( respectively SA , = NA , = E ( 0 ) A , = 0 if 0 € 7 ) . 7

spectral operator is of finite type if and only if it is annihilated by some power of its

...

6

**COROLLARY**. If A . T = 0 ( respectively TA , = 0 ) , then A , S = AN = A , E ( 0 ) =0 if 0 € 7 ( respectively SA , = NA , = E ( 0 ) A , = 0 if 0 € 7 ) . 7

**COROLLARY**. Aspectral operator is of finite type if and only if it is annihilated by some power of its

...

Page 2192

This shows that o ( $ ( J ) ) 25 ( 0 ) 2 n 1 ( 8 ) and completes the proof of the

lemma , Q . E . D . 12

complete B - space X . Suppose that A is topologically and algebraically

isomorphic ...

This shows that o ( $ ( J ) ) 25 ( 0 ) 2 n 1 ( 8 ) and completes the proof of the

lemma , Q . E . D . 12

**COROLLARY**. Let A be an algebra of operators in a weaklycomplete B - space X . Suppose that A is topologically and algebraically

isomorphic ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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