Linear Operators: General theory |
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Page 56
... homeomorphism in 9 , TM contains a non - void open set V. Thus , TGTM - T2 TM - T≥ V – V . Since a map of the form y → a → y is a homeomorphism , the set a open . Since the set V - V = ( a - V ) is the union of open sets , it is is ...
... homeomorphism in 9 , TM contains a non - void open set V. Thus , TGTM - T2 TM - T≥ V – V . Since a map of the form y → a → y is a homeomorphism , the set a open . Since the set V - V = ( a - V ) is the union of open sets , it is 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 , cq , 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 , cq , C [ 0 , 1 ] and the direct sum of these spaces ...
Page 442
... homeomorphism . Q.E.D. a 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 function a ...
... homeomorphism . Q.E.D. a 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 function a ...
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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