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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A counterexample to a question
of R. Haydon, E. Odell and H. Rosenthal


Author: G. Androulakis
Journal: Proc. Amer. Math. Soc. 126 (1998), 1425-1428
MSC (1991): Primary 46B25
MathSciNet review: 1452791
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Abstract: We give an example of a compact metric space $K$, an open dense subset $U$ of $K$, and a sequence $(f_n)$ in $C(K)$ which is pointwise convergent to a non-continuous function on $K$, such that for every $u \in U$ there exists $n \in \mathbf{N}$ with $f_n(u)=f_m(u)$ for all $m \geq n$, yet $(f_n)$ is equivalent to the unit vector basis of the James quasi-reflexive space of order 1. Thus $c_0$ does not embed isomorphically in the closed linear span $[f_n]$ of $(f_n)$. This answers in the negative a question asked by H. Haydon, E. Odell and H. Rosenthal.


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Additional Information

G. Androulakis
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Email: giorgis@math.missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04371-8
PII: S 0002-9939(98)04371-8
Received by editor(s): October 19, 1996
Additional Notes: This work is part of the author’s Ph.D. thesis, which was completed at the University of Texas at Austin in August 1996 under the supervision of Professor H. Rosenthal.
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society