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 ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he even used the term ...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 ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he even used the term ...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 xx satisfying ...
... 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 xx satisfying ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ