Abstract. The goal of this paper is to find the norm of special Gramians. As an illustrative example we determine the norm of the Hilbert matrix of infinite size using a method which is different from the usual one based on the Nehari extension problem (see [4]).

AMS Subject Classification (1991): 47B35, 15A60

Received April 29, 1998, and in revised form January 29, 1999. (Registered under 2711/2009.)