## Linear Operators: General theory |

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Page 17

A covering of a set A in a topological space X is a family of open sets whose union contains A. The space X is said to be

A covering of a set A in a topological space X is a family of open sets whose union contains A. The space X is said to be

**compact**if every covering of X ...Page 483

If T is weakly

If T is weakly

**compact**, then TS is**compact**in the Y * topology of Y and thus x ( TS ) is**compact**and hence closed in the Y * topology of Y ** .Page 494

From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly

From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly

**compact**set of rca ( S ) , and therefore T * is a weakly**compact**...### 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

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