The Unitary Equivalence Problem of Unilateral Weighted Shifts

Abstract:

      In this paper, we study the unilateral weighted shift which is unitarily equivalent to a Toeplitz operator and prove a similar result to that in [ 1 ] without the hypothesis that the shift must be hyponormal. As a corollary, we show that if the weight sequence {a_n}_n=0^∞ of the shift is convergent, then 1-a_n²=(1-a₀²)ⁿ⁺¹ ?n≥0