## Linear Operators: General theory |

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Page 91

admits an

admits an

**equivalent**metric under which it is complete , then G admits an invariant metric and is complete under each invariant metric .Page 311

According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is

According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is

**equivalent**to C ( S ) . Theorem 5.1 shows that there is ...Page 347

( b ) Show that L ( S , E , u ) is

( b ) Show that L ( S , E , u ) is

**equivalent**to l if and only if there exists a countable collection of atoms of finite measure { En } in such that every ...### 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