Linear Operators: General theory |
From inside the book
Results 1-3 of 78
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 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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