Linear Operators: General theory |
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Page 586
... Lemma 3 , there is a d1 such that if │μ ] < d1 , then ŪСo ( T ( μ ) ) . Let d≤ d be chosen such that | T ( 0 ) —T ( μ ) | < inf R ( 2 ; T ( 0 ) ) - 1 whenever u < d . It follows from Corollary 2 that λευ [ * ] R ( 2 ; T ( u ) ) = 00 R ...
... Lemma 3 , there is a d1 such that if │μ ] < d1 , then ŪСo ( T ( μ ) ) . Let d≤ d be chosen such that | T ( 0 ) —T ( μ ) | < inf R ( 2 ; T ( 0 ) ) - 1 whenever u < d . It follows from Corollary 2 that λευ [ * ] R ( 2 ; T ( u ) ) = 00 R ...
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 CP . 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 - group ...
... lemma . Q.E.D. We shall now state and prove the lemma referred to as CP . 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 - group ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ