Linear Operators: General theory |
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Page 88
... isometric isomorphism of X and X ** under the natural mapping z defined in 3.18 . James [ 4 , 5 ] has proved the following startling theorem . THEOREM . There exists a separable B - space which is isomorphic and isometric with its ...
... isometric isomorphism of X and X ** under the natural mapping z defined in 3.18 . James [ 4 , 5 ] has proved the following startling theorem . THEOREM . There exists a separable B - space which is isomorphic and isometric with its ...
Page 247
... isometric isomorphism of ( 12 ) * onto 12 . PROOF . It is clear that the mapping is an isomorphism . To see that it is also an isometric map we suppose first that 1 < p < ∞ . Then , from Minkowski's inequality ( III.3.3 ) , n n x * x ...
... isometric isomorphism of ( 12 ) * onto 12 . PROOF . It is clear that the mapping is an isomorphism . To see that it is also an isometric map we suppose first that 1 < p < ∞ . Then , from Minkowski's inequality ( III.3.3 ) , n n x * x ...
Page 313
... isometric isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . 1 ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all ba ( S1 , 1 ) . μ1 in PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that the ...
... isometric isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . 1 ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all ba ( S1 , 1 ) . μ1 in PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that the ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ