Vol. 69, No. 2, 1977

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Bicontractive projections and reordering of Lp-spaces

S. J. Bernau and Howard E. Lacey

Vol. 69 (1977), No. 2, 291–302

On a Banach space we call a projection, P, bicontractive, if P1 and I P1. In this paper we completely describe bicontractive projections on an Lp-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 p2, to describe all Banach lattices which are linearly isometric to an Lp-space.

Mathematical Subject Classification 2000
Primary: 46E30
Secondary: 46B99
Received: 24 June 1975
Published: 1 April 1977
S. J. Bernau
Howard E. Lacey