## 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 1994

Then , by Theorem 4 , ang = F - 1Ăn X , and since and

the continuity of F that m.100 lim S p ^ n ( 8 ) – ( 8 ) ] 2 ds = 0 , which implies ( III.

3.6 ) that in

then ...

Then , by Theorem 4 , ang = F - 1Ăn X , and since and

**converges**, we see fromthe continuity of F that m.100 lim S p ^ n ( 8 ) – ( 8 ) ] 2 ds = 0 , which implies ( III.

3.6 ) that in

**converges**in measure on o . Conversely , if ( 29 ) and ( 30 ) hold ,then ...

Page 2218

If a generalized sequence of projections in a o - complete Boolean algebra of

projections in a B - space

strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the case ...

If a generalized sequence of projections in a o - complete Boolean algebra of

projections in a B - space

**converges**weakly to a projection , then it**converges**strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the case ...

Page 2462

Moreover , if C belongs to the trace class 61 , then TnC

norm , and CT *

* / $ 1 } ) is conditionally compact , and thus for each ε > 0 there exists a finite ...

Moreover , if C belongs to the trace class 61 , then TnC

**converges**to zero in tracenorm , and CT *

**converges**to zero in trace norm . Proof . The set K = C ( { x € H ||* / $ 1 } ) is conditionally compact , and thus for each ε > 0 there exists a finite ...

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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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