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 fƒ a one - to - one continuous function on X , with f ( 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 fƒ a one - to - one continuous function on X , with f ( 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 X has a unique continuous extension f1 to S1 , and such that the correspondence f morphism of A and C ( S1 ) . * f is an isometric iso ...
... Hausdorff space S1 and a one - to - one embedding of S as a dense subset of S1 such that each f in X has a unique continuous extension f1 to S1 , and such that the correspondence f morphism of A and C ( S1 ) . * f is an isometric iso ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ