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 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 ƒ 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 ← f 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 X has a unique continuous extension f1 to S1 , and such that the correspondence f ← f is an isometric iso- morphism of A and C ( S1 ) ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ