Linear Operators: General theory |
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Page 48
... ( Theorem 2.7 ) . The proof of Theorem 2.5 goes back to Zermelo's [ 2 ] second proof of the well- ordering theorem . This paper is also interesting for its polemical dis- cussion of his axiom . The first occurrence of a maximum principle ...
... ( Theorem 2.7 ) . The proof of Theorem 2.5 goes back to Zermelo's [ 2 ] second proof of the well- ordering theorem . This paper is also interesting for its polemical dis- cussion of his axiom . The first occurrence of a maximum principle ...
Page 81
... Theorems 1.17 and 1.18 for B - spaces and gave [ 7 ] theorems related to these and the condensation theorem just mentioned for complete metric groups . ( See also Banach [ 1 ; Chap . 1 ] . ) The extension of Theorems 1.11 and 1.13 to F ...
... Theorems 1.17 and 1.18 for B - spaces and gave [ 7 ] theorems related to these and the condensation theorem just mentioned for complete metric groups . ( See also Banach [ 1 ; Chap . 1 ] . ) The extension of Theorems 1.11 and 1.13 to F ...
Page 82
Nelson Dunford, Jacob T. Schwartz. theorems or to give generalizations of some theorems of Saks [ 2 , 3 ] on sequences of ... theorem . THEOREM . Let U be a continuous function on Xx [ 0 , 1 ] to Y and such that for each t e [ 0 , 1 ] , U ...
Nelson Dunford, Jacob T. Schwartz. theorems or to give generalizations of some theorems of Saks [ 2 , 3 ] on sequences of ... theorem . THEOREM . Let U be a continuous function on Xx [ 0 , 1 ] to Y and such that for each t e [ 0 , 1 ] , U ...
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