## Linear Operators: General theory |

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Page 426

If X is a B - space , then the X topology of the closed

If X is a B - space , then the X topology of the closed

**unit sphere**S * of X * is a metric topology if and only if X is separable . PROOF . If X is separable , let { xn } be a countable dense subset of X , and define ( x * — y * x ...Page 458

If the closed

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

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 x is the natural embedding of X into X ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

91 other sections not shown

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