Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Isometries of non-commutative Lp-spaces

F. J. Yeadona1

a1 University of Hull

The spaces Lp(S0305004100058515_xs1D4D0, φ) for 1 ≤ p ≤ ∞, where φ is a faithful semifinite normal trace on a von Neumann algebra S0305004100058515_xs1D4D0, are defined in (10),(2),(14). The problem of determining the general form of an isometry S0305004100058515_inline1 of one such space into another has been studied in (i), (6), (9), (12), (5). Our main result, Theorem 2, is a characterization of such isometries for 1 ≤ p ≤ ∞, ≠ 2. The method of proof is based on that of (7), where isometries between Lp function spaces are characterized. The main step in the proof is Theorem 1, which gives the conditions under which equality holds in Clarkson's inequality.

(Received November 03 1980)