## Linear Operators: General theory |

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**Proof**. Let æ ** € ( L * ) * . By Theorem 1 , L * is isometrically isomorphic to Lq , so that there is a functional y * € L * such that x ** ( ** ) = y * ( g ) when g and x * are connected , as in Theorem 1 , by the formula ** 1 = { st ...Page 415

Hence ko e p - A , and thus p e A + ko CA + K . Q.E.D. Since the commutativity of the group G is not essential to the

Hence ko e p - A , and thus p e A + ko CA + K . Q.E.D. Since the commutativity of the group G is not essential to the

**proof**, the same result holds for non - Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear ...Page 434

and proceed as in the first part of the

and proceed as in the first part of the

**proof**of the preceding theorem to construct a subsequence { ym } of { xn } such that lim . , - X * ym exists for each r * in the set H of that**proof**. Let Km = co { ym , Ym + ] , .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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