Linear Operators: General theory |
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Page 289
... PROOF . This follows from Corollary 2 and Theorem II.3.28 . Q.E.D. Next we consider the problem of representing the ... PROOF . First assume μ ( S ) < ∞o . Then the steps in the proof of Theorem 1 apply without change through the point ...
... PROOF . This follows from Corollary 2 and Theorem II.3.28 . Q.E.D. Next we consider the problem of representing the ... PROOF . First assume μ ( S ) < ∞o . Then the steps in the proof of Theorem 1 apply without change through the point ...
Page 415
... proof , the same result holds for non - Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X : ( i ) co ( x4 ) a co ( 4 ) , co ( A + B ) = = If X is a linear topological space , then ( ii ) co ( A ) = co ...
... proof , the same result holds for non - Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X : ( i ) co ( x4 ) a co ( 4 ) , co ( A + B ) = = If X is a linear topological space , then ( ii ) co ( A ) = co ...
Page 434
... proof of the preceding theo- rem to construct a subsequence { ym } of { x } such that limm → ∞ x * Ym exists for each x * in the set H of that proof . Let Km Co { ym , Ym + 1 , ... } and let yo be an arbitrary point in Km . For each x ...
... proof of the preceding theo- rem to construct a subsequence { ym } of { x } such that limm → ∞ x * Ym exists for each x * in the set H of that proof . Let Km Co { ym , Ym + 1 , ... } and let yo be an arbitrary point in Km . For each x ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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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