Series: Mathematics Colloquium

Date: Thursday, September 5, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Arkady Tempelman

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Michael Lin, Ben-Gurion University, Beer-Sheva, Israel

Title: Ergodic Characterizations of Reflexivity of Banach Spaces

Abstract: 

A Banach space X is said to be mean ergodic if, for every
power-bounded linear operator T on X,

    lim_{n\to\infty} \frac1n \sum_{k=1}^n T^k x

exists for all x in X.  Lorch (1939) proved that all reflexive Banach
spaces are mean ergodic.  The converse is an open question.  We prove
the following theorem.  A Banach space X is reflexive if and only if
every closed subspace of X is mean ergodic.  This is joint work with
V. Fonf (Ben-Gurion University) and P. Wojtaszczyk (University of
Warsaw).