On unilateral weighted shifts in noncommutative operator theory

摘要

In this work, we investigate the condition for the functional model of unilateral weighted shift operator system. With the help of this model we also present the necessary and sufficient conditions for the algebra generated by this system to be isometrically isomorphic to the ball algebra. Over the last thirty years, there has been a great deal of development in the theory of non-selfadjoint operator algebras which play a crucial role in theoretical physics [1-3]. However, a general theory in this field has not yet been obtained. Therefore, understanding the structure of some of the non-selfadjoint operator algebras will be an important contribution to this area. In this paper, we will study the operator algebra generated by unilateral weighted shifts.