Linear Operators: General theory |
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Page 83
... sufficient conditions for the continuity of linear operators when the domain is a locally convex space . As may be surmised by analogy with the real case , additivity plus " measurability " of a function should imply continuity . That ...
... sufficient conditions for the continuity of linear operators when the domain is a locally convex space . As may be surmised by analogy with the real case , additivity plus " measurability " of a function should imply continuity . That ...
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 ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he even used the term ...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 ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he even used the term ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ