## Linear Operators: General theory |

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Page 48

The first occurrence of a maximum principle

The first occurrence of a maximum principle

**equivalent**to the well - ordering principle ( as in Theorem 2.6 ) is in Hausdorff ( 1 ; p . 140 ] . Zorn [ 1 ] gave a theorem essentially**equivalent**to Theorem 2.7 .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 . Thus every complete linear metric space can be metrized to be an F - space .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 measurable subset of S - u , En is either an atom of infinite measure or a null ...### 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