Ergodic characterization of reflexivity

A not so recent paper of Fonf, Lin and Wojtaszczyk (Journal of Functional Analysis Volume 187, Issue 1, 1 December 2001, Pages 146-162) proved that any ergodic Banach space with a (Schauder) basis is reflexive solving partially an open question of Sucheston posted more that 40 years ago.

A reasonable question is if we can extend this result when we consider ergodic Banach spaces not necessarily having a Schauder basis. The only know example of Banach spaces with no basis is due to Enflo (Acta Mathematica,Volume 130, Number 1 / july de 1973, Pages 309-317) and it is a non familiar space at all (actually it is a hard construction).


One thought on “Ergodic characterization of reflexivity

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s