Linear Operators: General theory |
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Page 56
... homeomorphism in , TM contains a non - void open set V. Thus , TGTM - T2TM - T≥ V – V . Since a map of the form y → a ― y is a homeomorphism , the set a - V is open . Since the set V - V U ( a - V ) is the union of open sets , it is ...
... homeomorphism in , TM contains a non - void open set V. Thus , TGTM - T2TM - T≥ V – V . Since a map of the form y → a ― y is a homeomorphism , the set a - V is open . Since the set V - V U ( a - V ) is the union of open sets , it is ...
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 , μ ) 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 , μ ) with ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ