A Toeplitz-like Operator with Rational Matrix Symbol Having Poles Only on the Unit Circle: The Adjoint, Symmetry and Fredholm Characteristics

Abstract In this paper we continue our investigation of unbounded Toeplitz operators whose symbols are rational matrix valued functions with poles on the unit circle, which was initiated in [16]. We further develop state space realization techniques for the symbols of these unbounded Toeplitz operators, and use the techniques to get more concrete results on the action, kernel and range, as well as the adjoint operator. These results are then used to determine Fredholm characteristics, and to det