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 , 1 € 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 , 1 € 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 * . 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 * . 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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ