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Page 249
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity | x + y2 + \ x — y | 2 = 2x2 + 2 | y | 2 , x , ye H , called the parallelogram identity , follows immediately from the axioms . If 8 = inf x - k❘ the preceding identity shows that ...
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity | x + y2 + \ x — y | 2 = 2x2 + 2 | y | 2 , x , ye H , called the parallelogram identity , follows immediately from the axioms . If 8 = inf x - k❘ the preceding identity shows that ...
Page 414
... identity , there is a neighborhood N of the identity such that N - NC M. 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 - NC M. Thus , any neighborhood of k 414 V.2.2 V. CONVEX SETS AND WEAK TOPOLOGIES.
Page 479
... identity on X * . Thus ( T * ) - 1 exists , is in B ( X * , Y * ) , and equals ( T - 1 ) * . Conversely , if ( T ... identity ( Tx , y ) = ( x , T VI.2.6 479 ADJOINTS Adjoints.
... identity on X * . Thus ( T * ) - 1 exists , is in B ( X * , Y * ) , and equals ( T - 1 ) * . Conversely , if ( T ... identity ( Tx , y ) = ( x , T VI.2.6 479 ADJOINTS Adjoints.
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ