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1. Introduction. In this note we consider a class of (bounded) operators on Hilbert space that properly contains the much-studied class of Toeplitz operators, and we show that virtually all of the results of  concerning spectral properties of Toeplitz operators are valid for operators in this larger class. We devote §2 to preliminary definitions and examples. The concept of a "Riesz system" is first introduced and then is used to define the class of generalized Toeplitz operators. Severaldoi:10.2307/1994279 fatcat:u6pgsf3j6zdkxpcx7bbpbkkgmi