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A weak Asplund space whose dual is not in Stegall's class
Author(s):
Ondrej
F. K.
Kalenda
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2139-2143.
MSC (2000):
Primary 54C60, 26E25, 54C10
Posted:
February 27, 2002
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Abstract:
We show that, under some additional set-theoretical assumptions which are equiconsistent with the existence of a measurable cardinal, there is a weak Asplund space whose dual, equipped with the weak* topology, is not in Stegall's class. This completes a result by Kenderov, Moors and Sciffer.
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Additional Information:
Ondrej
F. K.
Kalenda
Affiliation:
Department of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email:
kalenda@karlin.mff.cuni.cz
DOI:
10.1090/S0002-9939-02-06625-X
PII:
S 0002-9939(02)06625-X
Keywords:
Weak Asplund space,
fragmentable space,
Stegall's class of spaces
Received by editor(s):
April 5, 2000
Posted:
February 27, 2002
Additional Notes:
Partially supported by research grants GAUK 277/2001, GACR 201/00/1466 and MSM 113200007.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2002,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Preiss, D., Geometric measure theory in Banach spaces, Handbook of the geometry of Banach spaces, Vol. 2, North-Holland, Amsterdam, 2003, pp. 1519--1546. MR 2004f:46051
Moors, W.B. and Somasundaram, S., Some recent results concerning weak Asplund spaces, Acta Univ. Carolin. Math. Phys. 43 (2002), 67-86. MR MR1979559 (2004e:46027)
Moors, W.B. and Somasundaram, S., A weakly Stegall space that is not a Stegall space, Proc. Amer. Math. Soc. 131 (2003), 647-654. MR MR1933358 (2003h:54021)
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