Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

A remark on the tensor product of two maximal operator spaces

Christian Le Merdya1

a1 Equipe de Mathématiques, URA CNRS 741, Université de Franche-Comté, F-25030 Besançon Cedex, France

Abstract

Given a Banach space E, let us denote by Max(E) the largest operator space structure on E. Recently Paulsen-Pisier and, independently, Junge proved that for any Banach spaces E, F, S0013091500023816_inline1 isomorphically where S0013091500023816_inline2 and S0013091500023816_inline3 respectively denote the Haagerup tensor product and the spatial tensor product of operator spaces. In this paper we show that, in general, this equality does not hold completely isomorphically.

(Received September 20 1995)