Linear Operators: General theory |
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Page 88
... sufficient . Bonsall [ 1 ] showed that the separa- bility condition cannot be dropped . Ingleton [ 1 ] has given ... sufficient condition for reflexivity is given in Theorem V.4.7 . It is a consequence of Theorem V.6.1 that a necessary ...
... sufficient . Bonsall [ 1 ] showed that the separa- bility condition cannot be dropped . Ingleton [ 1 ] has given ... sufficient condition for reflexivity is given in Theorem V.4.7 . It is a consequence of Theorem V.6.1 that a necessary ...
Page 383
... sufficient to assure the continuity of the limit function . ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he even used the term ...
... sufficient to assure the continuity of the limit function . ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he even used the term ...
Page 472
... sufficient con- ditions for strong differentiability of the norm . THEOREM . In order that the norm is strongly differentiable at a point x in a B - space X , it is necessary and sufficient that every sequence of elements x * € X ...
... sufficient con- ditions for strong differentiability of the norm . THEOREM . In order that the norm is strongly differentiable at a point x in a B - space X , it is necessary and sufficient that every sequence of elements x * € 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 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