## Linear Operators: General theory |

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Page 540

Grothendieck showed there is a one - to - one correspondence between weakly

compact operators on C ( S ) to X and certain vector measures but did not use

this correspondence to

employed ...

Grothendieck showed there is a one - to - one correspondence between weakly

compact operators on C ( S ) to X and certain vector measures but did not use

this correspondence to

**represent**them . This integral**representation**wasemployed ...

Page 552

A question related to the

space . Gowurin gave a

...

A question related to the

**representation**of linear operators is that dealing with the**representation**of linear functions defined on certain spaces with values in a B -space . Gowurin gave a

**representation**for the general bounded linear functional...

Page 686

... is a class of equivalent functions and two functions fa and a

point if fa ( s ) = && ( 8 ) except on a u ... measurable with respect to the product of

Lebesgue measure and u ) and such a measurable

... is a class of equivalent functions and two functions fa and a

**represent**the samepoint if fa ( s ) = && ( 8 ) except on a u ... measurable with respect to the product of

Lebesgue measure and u ) and such a measurable

**representation**is unique ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero