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 ) | < ε , † € A } , where pe X , A is a finite subset of I ... 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 ) | < ε , † € A } , where pe X , A is a finite subset of I ... 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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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