 
Summary: A SUBSEQUENCE CHARACTERIZATION OF SEQUENCES
SPANNING ISOMORPHICALLY POLYHEDRAL BANACH SPACES
G. ANDROULAKIS
Abstract: Let (xn) be a sequence in a Banach space X which does not converge in
norm, and let E be an isomorphically precisely norming set for X such that
n
x
(xn+1  xn) < , x
E. ()
Then there exists a subsequence of (xn) which spans an isomorphically polyhedral
Banach space. It follows immediately from results of V. Fonf that the converse is also
true: If Y is a separable isomorphically polyhedral Banach space then there exists a
normalized Mbasis (xn) which spans Y and there exists an isomorphically precisely
norming set E for Y such that () is satisfied. As an application of this subsequence
characterization of sequences spanning isomorphically polyhedral Banach spaces we
obtain a strengthening of a result of J. Elton, and an OrliczPettis type result.
Acknowledgments: I would like to thank Professor H. Rosenthal for suggesting this
project to me and for his help. Also, I would like to thank Professors N. J. Kalton and
G. Godefroy for their comments, and Professor V. Fonf for the simplifications that he
suggested.
