Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
A SUBSEQUENCE CHARACTERIZATION OF SEQUENCES SPANNING ISOMORPHICALLY POLYHEDRAL BANACH SPACES
 

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 M-basis (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 Orlicz-Pettis 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.

  

Source: Androulakis, George - Department of Mathematics, University of South Carolina

 

Collections: Mathematics