In recent work byV. Milman and the author, the notions of weak cotype 2 and weak type 2 Banach spaces have been implicitly introduced. We investigate here the class of Banach spaces which are both of weak cotype 2 and weak type 2, which we call weak Hilbert spaces. These spaces can be characterized in a number of ways which will be described in this paper. Our results also suggest all kinds of questions which deserve further investigation. 1988 National Association of Social Workers, Inc.
