## 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 2064

... where \ S \ , is the L ,

subalgebra of A , but if we renorm it by placing ( 6 ) | al1 = lal + \ f | 1 then the

completeness of L , assures the completeness of A , under the

inequality ( 5 ) ...

... where \ S \ , is the L ,

**norm**of f . The algebra A , is not complete as asubalgebra of A , but if we renorm it by placing ( 6 ) | al1 = lal + \ f | 1 then the

completeness of L , assures the completeness of A , under the

**norm**( 6 ) and theinequality ( 5 ) ...

Page 2070

... is a B - space under the

in X. We let A , consist of all operators in H which have the form ( 17 ) a = ae + f ,

fe Le Theorem 1 shows that the operator a determines a and f uniquely , and so ...

... is a B - space under the

**norm**( 16 ) Iflo = \ f11 + If , fe Lo , where | f || is the**norm**in X. We let A , consist of all operators in H which have the form ( 17 ) a = ae + f ,

fe Le Theorem 1 shows that the operator a determines a and f uniquely , and so ...

Page 2462

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

* / $ 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 trace

**norm**, 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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