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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 | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [E] J. Elton, Extremely weakly unconditionally convergent series, Israel J. Math. 40 (1981), 255-258. MR 83e:46015
  • [HOR] R. Haydon, E. Odell, H. Rosenthal, On certain classes of Baire-1 functions with applications to Banach space theory, Lecture Notes in Mathematics Vol. 1470, Springer-Verlag, Berlin 1991. MR 92h:46018

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Additional Information

G. Androulakis
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211

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

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