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 ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841- he even used the term ...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 ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841- he even used the term ...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 392
... sufficient conditions for a set of measurable functions on [ 0 , 1 ] to be compact under this metric . ( Earlier , Veress [ 1 ] had given conditions assuring that a sequence of measurable functions has a uniformly convergent sub ...
... sufficient conditions for a set of measurable functions on [ 0 , 1 ] to be compact under this metric . ( Earlier , Veress [ 1 ] had given conditions assuring that a sequence of measurable functions has a uniformly convergent sub ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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