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Page 91
... equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in linear spaces . We have seen that in a normed ... equivalent invariant metric , but that an F - space may have no bounded sphere . Eidelheit and Mazur [ 1 ] have proved ...
... equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in linear spaces . We have seen that in a normed ... equivalent invariant metric , but that an F - space may have no bounded sphere . Eidelheit and Mazur [ 1 ] have proved ...
Page 311
... equivalent to C ( S1 ) . Theorem 5.1 shows that there is an isometric isomorphism * u between B * ( S , E ) and ba ( S , 2 ) , which is determined by the equation * E = u ( E ) , E e E. Thus , since B ( S , E ) is equivalent to C ( S1 ) ...
... equivalent to C ( S1 ) . Theorem 5.1 shows that there is an isometric isomorphism * u between B * ( S , E ) and ba ( S , 2 ) , which is determined by the equation * E = u ( E ) , E e E. Thus , since B ( S , E ) is equivalent to C ( S1 ) ...
Page 347
... equivalent to a closed subspace of a space ba ( S , 2 ) unless both are finite dimen- sional . 51 Show that no space L „ ( S , Σ , μ ) , 1 < p < ∞ , is equivalent either to a space C ( S ) or a space L1 ( S1 , E1 , 4 ) , unless it is ...
... equivalent to a closed subspace of a space ba ( S , 2 ) unless both are finite dimen- sional . 51 Show that no space L „ ( S , Σ , μ ) , 1 < p < ∞ , is equivalent either to a space C ( S ) or a space L1 ( S1 , E1 , 4 ) , unless it is ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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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