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Page 91
... homeomorphic to a normed linear space if and only if there exists a bounded convex neighborhood of the origin ... homeomorphism between each of the spaces L „ , lp , p ≥ 1 , c , Co , C [ 0 , 1 ] and the direct sum of these spaces ...
... homeomorphic to a normed linear space if and only if there exists a bounded convex neighborhood of the origin ... homeomorphism between each of the spaces L „ , lp , p ≥ 1 , c , Co , C [ 0 , 1 ] and the direct sum of these spaces ...
Page 157
... homeomorphism of ( u ) onto a subset of M ( S , Σ , μ ) . It is clear that this homeomorphism maps Cauchy sequences into Cauchy sequences . Thus if o ( En , Em ) → 0 , there is , by Corollary 6.5 , a function x in M ( S , Σ , u ) with ...
... homeomorphism of ( u ) onto a subset of M ( S , Σ , μ ) . It is clear that this homeomorphism maps Cauchy sequences into Cauchy sequences . Thus if o ( En , Em ) → 0 , there is , by Corollary 6.5 , a function x in M ( S , Σ , u ) with ...
Page 442
... homeomorphism . Q.E.D. ૨ 0 = 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an isometric isomorphism between C ( Q ) and C ( R ) . Then there exists a homeomorphism τ between R and Q , and a ...
... homeomorphism . Q.E.D. ૨ 0 = 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an isometric isomorphism between C ( Q ) and C ( R ) . Then there exists a homeomorphism τ between R and Q , and a ...
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