Homogeneous $2$-shifts

Abstract

The classification of homogeneous scalar weighted shifts is known. Recently, Korányi obtained a large class of inequivalent irreducible homogeneous bi-lateral $2$-by-$2$ block shifts. In this paper, we construct two distinct classes of examples not in the list of Korányi. It is then shown that these new examples of irreducible homogeneous bi-lateral $2$-by-$2$ block shifts, together with the ones found earlier by Korányi, account for every unitarily inequivalent irreducible homogeneous bi-lateral $2$-by-$2$ block shift.

26 pages