Linear Operators: General theory |
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Page 269
... topology is equivalent to the convergence of the scalars { fa ( 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 on F defined by ŝ ( f ) ...
... topology is equivalent to the convergence of the scalars { fa ( 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 on F defined by ŝ ( f ) ...
Page 430
... Weak Topologies . Weak Compactness We have already introduced and employed the concepts of weak sequential compactness ( II.3.25 ) and compactness in the X * ( or weak ) topology . There is at least one other type of weak compactness ...
... Weak Topologies . Weak Compactness We have already introduced and employed the concepts of weak sequential compactness ( II.3.25 ) and compactness in the X * ( or weak ) topology . There is at least one other type of weak compactness ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ