## Linear Operators: Spectral operators |

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Page 1951

Let T

0 € ö

7 and let To = TE ( 0 ) | E ( 0 ) X , the restriction of T to the invariant subspace E ...

Let T

**belong**to the right ( left ) ideal J in B ( X ) . Then every projection E ( 0 ) with0 € ö

**belongs**to J . If J is closed , then S and N also**belong**to J . PROOF . Let 0 €7 and let To = TE ( 0 ) | E ( 0 ) X , the restriction of T to the invariant subspace E ...

Page 2263

Under the hypotheses of the preceding theorem , every point deo , with the sole

possible exception of the point vo ,

spectral operator S . The point vo

spectrum ...

Under the hypotheses of the preceding theorem , every point deo , with the sole

possible exception of the point vo ,

**belongs**to the continuous spectrum of thespectral operator S . The point vo

**belongs**to the point or to the continuousspectrum ...

Page 2462

Moreover , if C

trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( {

XE H | | x 3 1 } ) is conditionally compact , and thus for each a > 0 there exists a

finite ...

Moreover , if C

**belongs**to the trace class C1 , then TnC converges to zero intrace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( {

XE H | | x 3 1 } ) is conditionally compact , and thus for each a > 0 there exists a

finite ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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