## Linear Operators: General theory |

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Page 40

For if I is maximal , then RļI is a commutative ring with

For if I is maximal , then RļI is a commutative ring with

**unit**which has no proper ideals ; by what we showed earlier R / I is a field .Page 458

5 If the closed

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

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 * is compact in the X ** topology of 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