Borel Maps with the "Point of Continuity Property" and Completely Borel Additive Families in Some Nonmetrizable Spaces

1994 ◽  
Vol 120 (3) ◽  
pp. 951 ◽  
Author(s):  
Petr Holicky
Keyword(s):  
Continuity Property ◽  
Point Of Continuity Property

A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property

1989 ◽  
Vol 32 (3) ◽  
pp. 274-280
Author(s):  
D. E. G. Hare
Keyword(s):  
Banach Spaces ◽  
Continuity Property ◽  
Dual Spaces ◽  
Equivalent Norms ◽  
Fréchet Differentiability ◽  
New Type ◽  
Frechet Differentiability ◽  
Point Of Continuity Property ◽  
Convex Point

AbstractWe introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established.

scholarly journals Weak-star point of continuity property and Schauder bases

2013 ◽  
Vol 219 (3) ◽  
pp. 225-236
Author(s):  
Ginés López-Pérez ◽  
José A. Soler-Arias
Keyword(s):  
Continuity Property ◽  
Weak Star ◽  
Schauder Bases ◽  
Point Of Continuity Property

scholarly journals Phelps spaces and finite dimensional decompositions

1988 ◽  
Vol 37 (2) ◽  
pp. 263-271 ◽  
Author(s):  
R. Deville ◽  
G. Godefroy ◽  
D.E.G. Hare ◽  
V. Zizler
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Continuity Property ◽  
Finite Dimensional ◽  
Point Of Continuity Property ◽  
Convex Point

We show that if X is a separable Banach space such that X* fails the weak* convex point-of-continuity property (C*PCP), then there is a subspace Y of X such that both Y* and (X/Y)* fail C*PCP and both Y and X/Y have finite dimensional Schauder decompositions.

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