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Page 413
non - zero linear functional on the complex space X , which separates the sets M and N. Q.E.D. 2. Linear Topological Spaces In this section , the results of Section 1 are applied to linear topological spaces .
non - zero linear functional on the complex space X , which separates the sets M and N. Q.E.D. 2. Linear Topological Spaces In this section , the results of Section 1 are applied to linear topological spaces .
Page 419
Then the I topology of X is the topology obtained by taking as base all sets of the form N ( p ; A , ε ) = { q ... If I ' is a total linear space of linear functionals on X , X is a locally convex linear topological space in its 1 ...
Then the I topology of X is the topology obtained by taking as base all sets of the form N ( p ; A , ε ) = { q ... If I ' is a total linear space of linear functionals on X , X is a locally convex linear topological space in its 1 ...
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6 ( 308 ) Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic properties of , Chap . II definition , II . ... of C - spaces , V . 8 . 8 ( 442 ) remarks on , ( 396 - 397 , 466 ) Base for a topology , criterion for ...
6 ( 308 ) Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic properties of , Chap . II definition , II . ... of C - spaces , V . 8 . 8 ( 442 ) remarks on , ( 396 - 397 , 466 ) Base for a topology , criterion for ...
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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