1983 paper, Rieffel introduced a Banach algebra counterpart to the
purely algebraic notion of the stable rank of an algebra: the
topological stable rank. He defined the left and right topological
stable rank of a unital Banach algebra and showed that these are equal
for a unital C*-algebra. He asked: must the left and right topological
stable rank always agree? We answer this question in the negative; our
counterexample is a nest algebra. This talk represents joint work with
Ken Davidson, Laurent Marcoux and Heydar Radjavi.