Linear Operators: General theory |
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Page 156
... shown that the conjugate spaces of some familiar B - spaces may be represented in terms of set functions . In the present section it will be shown that the spaces of bounded additive set func- tions , and regular countably additive set ...
... shown that the conjugate spaces of some familiar B - spaces may be represented in terms of set functions . In the present section it will be shown that the spaces of bounded additive set func- tions , and regular countably additive set ...
Page 312
... shown that T ( E ) is open and closed for E e E. Conversely , let E , be any open and closed set in S1 . We wish to show that the set ET - 1 ( E ) is in E. Since XE is E - measurable , there exists a finite decomposition of S into ...
... shown that T ( E ) is open and closed for E e E. Conversely , let E , be any open and closed set in S1 . We wish to show that the set ET - 1 ( E ) is in E. Since XE is E - measurable , there exists a finite decomposition of S into ...
Page 335
... shown that W satisfies the hypothesis of Zorn's lemma . To do this we let Wo be a totally ordered subset of W ( I.22 ) and let c CUW 。. Then , for some a e Wo , ca is not void . Let a be the smallest element of coa and let y be any ...
... shown that W satisfies the hypothesis of Zorn's lemma . To do this we let Wo be a totally ordered subset of W ( I.22 ) and let c CUW 。. Then , for some a e Wo , ca is not void . Let a be the smallest element of coa and let y be any ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ