Examples concerning heredity problems of WCG Banach spaces
Authors:
Spiros A. Argyros and Sophocles Mercourakis
Journal:
Proc. Amer. Math. Soc. 133 (2005), 773785
MSC (2000):
Primary 46B20, 46B26, 03E05
Published electronically:
August 20, 2004
MathSciNet review:
2113927
Fulltext PDF Free Access
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Additional Information
Abstract: We present two examples of WCG spaces that are not hereditarily WCG. The first is a space with an unconditional basis, and the second is a space such that is WCG and does not contain . The nonWCG subspace of has the additional property that is not WCG and is reflexive.
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 [HHZ]
 P. Habala, P. Hajek, and V. Zizler, Introduction to Banach Spaces I, II Matfyzpress, Prague (1996).
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 J. Hagler and E. Odell, A Banach space not containing whose dual ball is not weaksequentially compact, Illinois J. Math. 22, (1978), 290294. MR 58:2174
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 R.C. James, A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc. 80, (1974), 738743. MR 54:5811
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Additional Information
Spiros A. Argyros
Affiliation:
Department of Mathematics, National Technical University of Athens, Athens 15780, Greece
Email:
sargyros@math.ntua.gr
Sophocles Mercourakis
Affiliation:
Department of Mathematics, University of Athens, Athens 15784, Greece
Email:
smercour@math.uoa.gr
DOI:
http://dx.doi.org/10.1090/S000299390407532X
PII:
S 00029939(04)07532X
Keywords:
WCG Banach space,
unconditional basis,
tree
Received by editor(s):
July 16, 2003
Received by editor(s) in revised form:
October 23, 2003
Published electronically:
August 20, 2004
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2004
American Mathematical Society
