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Page 36
A linear vector space , linear space , or vector space over a field 0 is an additive group X together with an operation m : 0 X → X , written as m ( a , x ) = ax , which satisfy the following four conditions : ( i ) a ( x + y ) = aut + ...
A linear vector space , linear space , or vector space over a field 0 is an additive group X together with an operation m : 0 X → X , written as m ( a , x ) = ax , which satisfy the following four conditions : ( i ) a ( x + y ) = aut + ...
Page 250
If y * # 0 the set M = { wy * x = 0 } is a proper closed linear manifold in H and its orthocomplement N contains , by Lemma 4 , a vector 41 + 0. Let y = ayı where a = y * ( y ) / | y1 | 2 . For an arbitrary vector x in H the vector x- ...
If y * # 0 the set M = { wy * x = 0 } is a proper closed linear manifold in H and its orthocomplement N contains , by Lemma 4 , a vector 41 + 0. Let y = ayı where a = y * ( y ) / | y1 | 2 . For an arbitrary vector x in H the vector x- ...
Page 795
Compact metric Boolean algebras and vector lattices . J. Sci . Hirosima Univ . Ser . A. 11 , 125–128 ( 1942 ) . 2. On Fréchet lattices , I. J. Sci . Hirosima Univ . Ser . A. 12 , 235-248 ( 1943 ) . ( Japanese ) Math . Rev.
Compact metric Boolean algebras and vector lattices . J. Sci . Hirosima Univ . Ser . A. 11 , 125–128 ( 1942 ) . 2. On Fréchet lattices , I. J. Sci . Hirosima Univ . Ser . A. 12 , 235-248 ( 1943 ) . ( Japanese ) Math . Rev.
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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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