Linear Operators: General theory |
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Page 18
... space to a Hausdorff space is a homeomorphism . PROOF . Let X be a compact space , Y a Hausdorff space , and ƒ a one - to - one continuous function on X , with ƒ ( X ) = Y. According to the preceding lemma , a closed set A in X is ...
... space to a Hausdorff space is a homeomorphism . PROOF . Let X be a compact space , Y a Hausdorff space , and ƒ a one - to - one continuous function on X , with ƒ ( X ) = Y. According to the preceding lemma , a closed set A in X is ...
Page 274
... Hausdorff space and C ( S ) be the algebra of all complex continuous functions on S. Let A be a closed subalgebra of ... space B ( S ) and the space of continuous functions on a certain compact Hausdorff space . The space B ( S ) is an ...
... Hausdorff space and C ( S ) be the algebra of all complex continuous functions on S. Let A be a closed subalgebra of ... space B ( S ) and the space of continuous functions on a certain compact Hausdorff space . The space B ( S ) is an ...
Page 276
... Hausdorff space S1 and a one - to - one embedding of S as a dense subset of S1 such that each f in A has a unique continuous extension f1 to S1 , and such that the correspondence f → f1 is an isometric iso- morphism of A and C ( S1 ) ...
... Hausdorff space S1 and a one - to - one embedding of S as a dense subset of S1 such that each f in A has a unique continuous extension f1 to S1 , and such that the correspondence f → f1 is an isometric iso- morphism of A and C ( S1 ) ...
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