## 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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**Corollary**VI.5.5 the compact operators form a closed twosided ideal in B ( x ) and so the present**corollary**is immediate . Q.E.D. 4**COROLLARY**. If T is weakly compact , then so are S , N , and every projection E ( 0 ) with 0 $ .Page 1952

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**COROLLARY**. If A , T = 0 ( respectively TA , = 0 ) , then A , S = A , N = A , E ( 0 ) = 0 if 0 ( respectively SA = NA . = E ( 0 ) 4. = 0 if 0 € 0 ) .**COROLLARY**. A spectral operator is of finite type if and only if it is annihilated ...Page 2192

This shows that O ( S ( f ) ) 2f ( o ) 2 n f ( 8 ) E ( O ) = 1 and completes the proof of the lemma , Q.E.D. 12

This shows that O ( S ( f ) ) 2f ( o ) 2 n f ( 8 ) E ( O ) = 1 and completes the proof of the lemma , Q.E.D. 12

**COROLLARY**. Let A be an algebra of operators in a weakly complete B - space X. Suppose that A is topologically and ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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