## 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

It follows from Theorem 11.4 that ( 5 ) lal < l « l + 1fli , where \ f | , is the L ,

It follows from Theorem 11.4 that ( 5 ) lal < l « l + 1fli , where \ f | , is the L ,

**norm**of f . The algebra A , is not complete as a subalgebra of A , but if we renorm it by placing ( 6 ) lal1 = 10 + 1f11 , then the completeness of Lį ...Page 2070

It is clear that A , is a B - space under this

It is clear that A , is a B - space under this

**norm**. It is also an algebra , for the product of two operators a = de + f and b = Be + g in A , is ( 19 ) ab = aße + ag + Bf + h , where h = f * g is in Lo by ( 15 ) .Page 2462

Moreover , if C belongs to the trace class C1 , then T , C converges to zero in trace

Moreover , if C belongs to the trace class C1 , then T , C converges to zero in trace

**norm**, and CT * converges to zero in trace**norm**. PROOF . The set K = C ( { x H || æ $ 1 } ) is conditionally compact , and thus for each ε > 0 there ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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