Rotation operators with multiplication and some of their generalizations (Q750851)

The author generalizes results about the description of the spectrum of a weighted rotational operator acting in the Hardy space. He proposes an abstract scheme of the investigation of an operator aU, where a bounded linear operator a belongs to some commutative Banach operator algebra A, U is an invertible isometric operator, furthermore the algebra A and the operator U satisfy some additional assumptions. Several concrete examples of this abstract situation are considered.