## Linear Operators: General theory |

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Page 426

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

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 .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 ...Page 485

Since the closed unit

Since the closed unit

**sphere**S * of Y * is Y - compact ( V.4.2 ) ... If S , S ** are the closed unit**spheres**in X , X ** , respectively , and if x is the ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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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 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