Hamburger-type weighted shifts: Jumping flatness and Aluthge transforms

초록

In- this paper, we introduce a new kind of flatness, namely "jumping flatness," of a Hamburger-type weighted shift; we characterize jumping flatness of a nonsubnormal Hamburger-type weighted shift W-alpha and obtain the expression of the associated Hamburger moment measure. Also we discuss a relationship between jumping flatness and subnormality of the Aluthge transform (W) over tilde (alpha). Precisely, we show that if W-alpha is a nonsubnormal Hamburger-type weighted shift, then W-alpha has jumping flatness if and only if there exist positive real numbers phi, phi, rho, p, and q such that mu = phi delta(-p) + phi delta(0) + rho delta(q) (or mu = phi delta(-p) +rho delta(q)) and (W) over tilde (alpha). is subnormal, where delta(x) is the usual Dirac measure. (C) 2020 Elsevier Inc. All rights reserved.

키워드