Abstract. The abstract analogue of classical two variables Toeplitz operators is presented. The existence of symbol operators is shown. Properties of the doubly commuting minimal isometric dilation of doubly commuting contractions are used.

AMS Subject Classification (1991): 47A62, 47A20,47B35, 47B38, 47B20

Keyword(s): Contraction, isometric dilation, doubly commuting, Toeplitz operator, symbol operator

Received June 26, 2003, and in final form October 4, 2004. (Registered under 5873/2009.)