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. 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. 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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ