MLUR renormings of Banach spaces

Patrick Dowling, Zhibao Hu and Mark Andrew Smith

Vol. 170 (1995), No. 2, 473–482

DOI: 10.2140/pjm.1995.170.473

Abstract

A specific construction is given on a Banach space X with a 1-unconditional basis which yields an equivalent norm on X that is midpoint locally uniformly rotund. This construction, when applied to ℓ², confirms a suspicion of K. W. Anderson and answers a question of R. E. Megginson; when applied to an example of M. Talagrand, it improves an example of P.-K. Lin.

Mathematical Subject Classification 2000

Primary: 46B03

Secondary: 46B15, 46B20, 46B22

Milestones

Received: 12 February 1993

Revised: 22 February 1994

Published: 1 October 1995