Properties of two variables Toeplitz type operators

Abstract

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.

Keywords

• pair of contractions
• isometric dilation
• doubly commuting
• Toeplitz operator
• symbol operator