LAUSR

Given a unilateral forward shift S acting on a complex, separable, innite dimensional Hilbert space H, an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that {S*nTSn} is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H. In this paper, we study the asymptotic Tu-Toeplitzness of weighted composition operators on the Hardy space H2, where u is a nonconstant inner function.