Linear Operators: General theory |
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Page 88
... isometric isomorphism of X and X ** under the natural mapping x 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 x 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 ( 17 ) * onto l2 . 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 ( 17 ) * onto l2 . 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 . 22 ) . ( c ) If E is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all M1 in ba ( S1 , 21 ) . PROOF . Recalling that 7 is an isomorphism of Σ onto E1 , it is clear that the ...
... isometric isomorphism of ba ( S1 , E1 ) onto ca ( S1 . 22 ) . ( c ) If E is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all M1 in ba ( S1 , 21 ) . PROOF . Recalling that 7 is an isomorphism of Σ onto E1 , it is clear that the ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ