Linear Operators: General theory |
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Page 410
... lemma is an obvious consequence of Definition 1 . 2 LEMMA . The intersection of an arbitrary family of convex subsets of the linear space X is convex . As examples of convex subsets of X , we note the subspaces of X , and the subsets of ...
... lemma is an obvious consequence of Definition 1 . 2 LEMMA . The intersection of an arbitrary family of convex subsets of the linear space X is convex . As examples of convex subsets of X , we note the subspaces of X , and the subsets of ...
Page 697
... Lemma 11 will be an inductive one based upon its special case k = 1 which has been established in Lemma 6. Since the proof is a rather circuitous one , based upon three auxiliary lemmas , it will perhaps be of some help if we make a ...
... Lemma 11 will be an inductive one based upon its special case k = 1 which has been established in Lemma 6. Since the proof is a rather circuitous one , based upon three auxiliary lemmas , it will perhaps be of some help if we make a ...
Page 699
... lemma . Q.E.D. We shall now state and prove the lemma referred to as CPk . For technical reasons occurring later the following lemma is stated for what might be called a positive sub - semi - group rather than for a positive semi ...
... lemma . Q.E.D. We shall now state and prove the lemma referred to as CPk . For technical reasons occurring later the following lemma is stated for what might be called a positive sub - semi - group rather than for a positive semi ...
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