Linear Operators: General theory |
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Page 81
... give those theorems or to give generalizations of some theorems of Saks II.5 81 NOTES AND REMARKS.
... give those theorems or to give generalizations of some theorems of Saks II.5 81 NOTES AND REMARKS.
Page 82
... give a very simple proof of the uniform boundedness theorem for B - spaces . Bourbaki [ 3 ] has demonstrated that Theorem 1.17 remains valid in a certain class of locally convex topological linear spaces . ( See also Dieudonné and ...
... give a very simple proof of the uniform boundedness theorem for B - spaces . Bourbaki [ 3 ] has demonstrated that Theorem 1.17 remains valid in a certain class of locally convex topological linear spaces . ( See also Dieudonné and ...
Page 503
... give several applications of Theorem 2 . The first makes use of the compactness Theorem V.4.3 to give the general form of a mapping from L1 ( S , Σ , μ ) to the conjugate of a separable space . 6 THEOREM . Let ( S , E , μ ) be a o ...
... give several applications of Theorem 2 . The first makes use of the compactness Theorem V.4.3 to give the general form of a mapping from L1 ( S , Σ , μ ) to the conjugate of a separable space . 6 THEOREM . Let ( S , E , μ ) be a o ...
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