Bicontractive projections and reordering of L_p-spaces

S. J. Bernau and Howard E. Lacey

Vol. 69 (1977), No. 2, 291–302

DOI: 10.2140/pjm.1977.69.291

Abstract

On a Banach space we call a projection, P, bicontractive, if ∥P∥≦ 1 and ∥I − P∥≦ 1. In this paper we completely describe bicontractive projections on an L_p-space (1 ≦ p < ∞) by showing that for every such bicontractive projection P, 2P − I is an involutive linear isometry. Duality then gives the same result for pre-dual L₁-spaces (in particular for M-spaces). The analysis of bicontractive projections is used, with p≠2, to describe all Banach lattices which are linearly isometric to an L_p-space.

Mathematical Subject Classification 2000

Primary: 46E30

Secondary: 46B99

Milestones

Received: 24 June 1975

Published: 1 April 1977