## Linear Operators: General theory |

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Page 238

During the course of the investigation a number of interesting special properties

of the spaces to be considered and certain ... 1 The space En is the

of ordered n - tuples x = [ CD , . . . , an ] of scalars dj , . . . , Om . The norm is \ w ...

During the course of the investigation a number of interesting special properties

of the spaces to be considered and certain ... 1 The space En is the

**linear space**of ordered n - tuples x = [ CD , . . . , an ] of scalars dj , . . . , Om . The norm is \ w ...

Page 410

The intersection of an arbitrary family of convex subsets of the

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 . Let x1 , . . . , Xn be points in ...

The intersection of an arbitrary family of convex subsets of the

**linear space**X isconvex . As examples of convex subsets of X , we note the subspaces of X , and

the subsets of X consisting of one point . 3 LEMMA . Let x1 , . . . , Xn be points in ...

Page 838

( See also Hamel base ) in a B - space , criterion for compactness with , IV . 5 . 5 (

260 ) definition , II . 4 . 7 ( 71 ) properties , II . 4 . 8 - 12 ( 71 ) remarks on , ( 93 – 94

) in a

( See also Hamel base ) in a B - space , criterion for compactness with , IV . 5 . 5 (

260 ) definition , II . 4 . 7 ( 71 ) properties , II . 4 . 8 - 12 ( 71 ) remarks on , ( 93 – 94

) in a

**linear space**. ( See Hamel base ) orthogonal and orthonormal bases in ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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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 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