Linear Operators: General theory |
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Page 269
... topology is equivalent to the convergence of the scalars { f ( s ) } for each s e S. The relative product topology on F is seen to be the weakest topology on F in which each s e S generates a continuous function ŝ on F defined by ŝ ( f ) ...
... topology is equivalent to the convergence of the scalars { f ( s ) } for each s e S. The relative product topology on F is seen to be the weakest topology on F in which each s e S generates a continuous function ŝ on F defined by ŝ ( f ) ...
Page 477
... weak operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the weak operator topology in B ( X , Y ) . 4 THEOREM . A linear ...
... weak operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the weak operator topology in B ( X , Y ) . 4 THEOREM . A linear ...
Page 512
... weak operator topology , Y is reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak topology on every positive multiple aS of the closed unit sphere S of B ( X , Y ) . Show by ...
... weak operator topology , Y is reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak topology on every positive multiple aS of the closed unit sphere S of B ( X , Y ) . Show by ...
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 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ