## Linear Operators: General theory |

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Page 238

Thus our zero

Thus our zero

**vector**will be the function which is identically zero . In the list below , we will not ordinarily specify whether the**spaces**are to consist ...Page 410

The intersection of an arbitrary family of convex subsets of the

The intersection of an arbitrary family of convex subsets of the

**linear space**X is convex . As examples of convex subsets of X , we note the subspaces of X ...Page 838

4 . 8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a

4 . 8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a

**linear space**. ( See Hamel base ) orthogonal and orthonormal bases in Hilbert space , definition , IV . 4 .### 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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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