## Linear Operators: General theory |

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Thus every complete linear metric space can be metrized to be an F - space . Further , a normed

Thus every complete linear metric space can be metrized to be an F - space . Further , a normed

**linear space**is a B - space provided it is complete under some equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] .Page 239

The space Inc is the

The space Inc is the

**linear space**of all ordered n - tuples [ cy , . .. , Cen ] of scalars Oy , ... , Olin with the norm lv sup laila 1 Sisn 4. The space l , is defined for 1 sp < oo as the**linear space**of all sequences x = { an } of ...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, and the subsets of X consisting of one point. 3 Lemma.### 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 continuous functions 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 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