The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.
Department of Applied Mathematics, University of Agriculture, ul. Balicka 253c, 30-198 Kraków, ; and Institute of Mathematics, Pedagogical University, ul. Podchorążych 2, 30-084 Kraków,