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Page 89
... B - algebras . Completion of spaces . In the definitions of F- and B - spaces , we required the spaces to be ... space satisfying properties ( i ) and ( ii ) of Definition 1.10 . Then X is isomorphic and isometric with a dense linear subspace ...
... B - algebras . Completion of spaces . In the definitions of F- and B - spaces , we required the spaces to be ... space satisfying properties ( i ) and ( ii ) of Definition 1.10 . Then X is isomorphic and isometric with a dense linear subspace ...
Page 398
... space . Let S be a Stone space and X C ( S ) the real continuous func- tions . Grothendieck [ 4 ; p . 168 ] showed that every X - convergent se- quence in * is actually ** - convergent , and that if Y is a separable B - space , then any ...
... space . Let S be a Stone space and X C ( S ) the real continuous func- tions . Grothendieck [ 4 ; p . 168 ] showed that every X - convergent se- quence in * is actually ** - convergent , and that if Y is a separable B - space , then any ...
Page 436
... space of linear functionals on X. 2 If X is an infinite dimensional B - space then X * ‡ X * . 3 Let X be a linear topological space . Then X has a non - zero continuous linear functional if and only if the origin is interior to some ...
... space of linear functionals on X. 2 If X is an infinite dimensional B - space then X * ‡ X * . 3 Let X be a linear topological space . Then X has a non - zero continuous linear functional if and only if the origin is interior to some ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ