Linear Operators: General theory |
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Page 8
... subsets of a set has the property that A € E if and only if every finite subset of A belongs to & , then & contains a maximal element . 3 Derive Theorem 6 from the statement of Exercise 2 . 4 Show that any one of the following implies ...
... subsets of a set has the property that A € E if and only if every finite subset of A belongs to & , then & contains a maximal element . 3 Derive Theorem 6 from the statement of Exercise 2 . 4 Show that any one of the following implies ...
Page 17
... subset of a normal space has a real continuous extension defined on the whole space . PROOF . The only case where the theorem does not apply imme- diately is the case where ƒ is unbounded . If ƒ is real and continuous on the closed set ...
... subset of a normal space has a real continuous extension defined on the whole space . PROOF . The only case where the theorem does not apply imme- diately is the case where ƒ is unbounded . If ƒ is real and continuous on the closed set ...
Page 456
... subset of a locally convex linear topological space has the fixed point property . PROOF . By Zorn's lemma there exists a minimal convex subset K1 of K with the property that TK1CK1 . By the previous lemma , this minimal subset contains ...
... subset of a locally convex linear topological space has the fixed point property . PROOF . By Zorn's lemma there exists a minimal convex subset K1 of K with the property that TK1CK1 . By the previous lemma , this minimal subset contains ...
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