## Linear Operators: General theory |

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Page 89

In the definitions of F- and B - spaces , we required the spaces to be complete in ... Let X be a

In the definitions of F- and B - spaces , we required the spaces to be complete in ... Let X be a

**linear space**satisfying properties ( i ) and ( ii ) of ...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.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, ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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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