## 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 * e L * such that *** ( ** ) = y ...Page 415

Hence ko € 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 € 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 ...Page 434

Ym m - 00 and proceed as in the first part of the

Ym m - 00 and proceed as in the first part of the

**proof**of the preceding theorem to construct a subsequence { ym } of { xn } such that limm + * . exists for ...### 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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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains 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 Hilbert space 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