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Page 35
... identity e is unique ; the inverse a1 of a is unique ; for every a and b in G , there are uniquely determined elements x and y in G for which ax b ; the unit e in G belongs to every subgroup of G ; and ( ab ) -1 = b - 1a - 1 . A mapping ...
... identity e is unique ; the inverse a1 of a is unique ; for every a and b in G , there are uniquely determined elements x and y in G for which ax b ; the unit e in G belongs to every subgroup of G ; and ( ab ) -1 = b - 1a - 1 . A mapping ...
Page 249
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity x + y2 + x - y2 = 2x2 + 2y2 , x , y ε H , called the parallelogram identity , follows immediately from the axioms . If 8 infx - k the preceding identity shows that - 3 - kЄK | k ― k ...
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity x + y2 + x - y2 = 2x2 + 2y2 , x , y ε H , called the parallelogram identity , follows immediately from the axioms . If 8 infx - k the preceding identity shows that - 3 - kЄK | k ― k ...
Page 414
... identity , there is a neighborhood N of the identity such that N - NCM . Thus , any neighborhood of k 414 V.2.2 V. CONVEX SETS AND WEAK TOPOLOGIES.
... identity , there is a neighborhood N of the identity such that N - NCM . Thus , any neighborhood of k 414 V.2.2 V. CONVEX SETS AND WEAK TOPOLOGIES.
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