## Linear Operators: Spectral operators |

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Results 1-3 of 98

Page 1951

By

and so the present

compact , then so are S , N , and every projection E ( o ) with 0 € 0 . PROOF .

By

**Corollary**V1.5.5 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 weaklycompact , then so are S , N , and every projection E ( o ) with 0 € 0 . PROOF .

Page 1952

6

0 if 0 € ö ( respectively SA , = NA , = E ( 0 ) A , = 0 if 0 ¢ o ) . 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 = A , N = A , E ( 0 ) =0 if 0 € ö ( respectively SA , = NA , = E ( 0 ) A , = 0 if 0 ¢ o ) . 7

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

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Page 2192

Q.E.D. 12

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

some B - algebra of bounded continuous functions . Then every operator in A is a

...

Q.E.D. 12

**COROLLARY**. Let A be an algebra of operators in a weakly completeB - space X. Suppose that A is topologically and algebraically isomorphic to

some B - algebra of bounded continuous functions . Then every operator in A is a

...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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