## Linear Operators: General theory |

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Page 88

x = p ( x ) + p ( -x ) , then this condition is

x = p ( x ) + p ( -x ) , then this condition is

**sufficient**. Bonsall [ 1 ] showed that the separability condition cannot be dropped . Ingleton [ 1 ] has given conditions for the Hahn - Banach theorem to hold when the field of scalars is ...Page 385

ing conditions that are

ing conditions that are

**sufficient**to insure that a class of functions generates the entire space . Wermer [ 6 , 9 ] has given**sufficient**conditions that two functions generate C ( S ) when S is the unit circle .Page 472

In the first two papers , necessary and

In the first two papers , necessary and

**sufficient**conditions for a weaker type of differentiability of the norms in X and X * are given , together with results relating differentiability , tangent planes to the unit sphere ...### 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