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 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 schematic ...
... Lemma 11 will be an inductive one based upon 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 schematic ...
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
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