Linear Operators: General theory |
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Page 419
... topology of X is the topology obtained by taking as base all sets of the form N ( p ; A , ε ) = { q || f ( p ) —f ( q ) | < ɛ , † € A } , where pe X , A is a finite subset of Land ... topology if and only if lim , x V.3.2 419 WEAK TOPOLOGIES.
... topology of X is the topology obtained by taking as base all sets of the form N ( p ; A , ε ) = { q || f ( p ) —f ( q ) | < ɛ , † € A } , where pe X , A is a finite subset of Land ... topology if and only if lim , x V.3.2 419 WEAK TOPOLOGIES.
Page 420
... topological space and X = Y * . In this case , what is known as the topology of Y * is ob- tained . The reader will have observed that in certain cases a number of different topologies have been defined for the same space X. For in ...
... topological space and X = Y * . In this case , what is known as the topology of Y * is ob- tained . The reader will have observed that in certain cases a number of different topologies have been defined for the same space X. For in ...
Page 512
... 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 the method of ...
... 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 the method of ...
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