Abstract. We prove that an operator valued positive definite function defined on an interval of ${\msbm Z}^2$ with the lexicographic order can be extended to a positive definite function on the whole discrete plane.

AMS Subject Classification (1991): 43A35, 47D03

Keyword(s): operator valued positive definite functions, semigroup of operators, lexicographic order

Received April 29, 1999, and in revised form November 8, 1999. (Registered under 2756/2009.)