## Linear Operators: General theory |

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Q.E.D. 6 COROLLARY . If x is the natural embedding of a B - space X into X ** , then rX is X * -dense in X ** . Proof . The X * -closure of 2 ( X ) is a subspace of X ** , which , by Theorem 5 , contains the unit

Q.E.D. 6 COROLLARY . If x is the natural embedding of a B - space X into X ** , then rX is X * -dense in X ** . Proof . The X * -closure of 2 ( X ) is a subspace of X ** , which , by Theorem 5 , contains the unit

**sphere**of X ** .Page 458

5 If the closed unit

5 If the closed unit

**sphere**of an infinite dimensional B - space X contains only a finite number of extremal points , then X is not isometrically isomorphic to the conjugate of any B - space . 6 Let S be a topological space , and let C ...Page 485

Since the closed unit

Since the closed unit

**sphere**S * of Y * is Y - compact ( V.4.2 ) , it follows from Lemma 7 and Lemma 1.5.7 that T * S ... If S , S ** are the closed unit**spheres**in X , X ** , respectively , and if ~ is the natural embedding of X into X ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc Proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero