Characterizations of a Complex Symmetric Truncated Backward Shift Type Operator Matrix and its Transforms

Abstract

In this paper we study characterizations of a complex symmetric truncated shift type operator matrix and the Aluthge transform, the Duggal transform, the mean transform, and the generalized mean transform of such an operator matrix T (see (2.1) or (2.2)). As some applications of our main results, we give several examples of truncated shift type operator matrices.