Abstract
For a positive integer m, a bounded linear operator T on a Hilbert space \(\mathbb {H}\) is called an (A, m)-isometry, if \(\Theta ^{(m)}_{A}(T) =\sum _{k=0}^{m}(-1)^{m-k}{m\atopwithdelims ()k}T^{*k}AT^{k}=0\), where A is a positive (semi-definite) operator. In this paper we give a characterization of (A, m)-isometric and strict (A, m)-isometric unilateral weighted shifts in terms of their weight sequences, respectively. Moreover, we characterize (A, 2)-expansive unilateral weighted shifts (i.e. operators satisfying \(\Theta ^{(2)}_{A}(T)\le 0\)).
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We would like to thank the referee for his/her useful comments in order to ameliorate the contents of the paper.
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Communicated by Rosihan M. Ali.
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Rabaoui, R., Saddi, A. (A, m)-Isometric Unilateral Weighted Shifts in Semi-Hilbertian Spaces. Bull. Malays. Math. Sci. Soc. 41, 371–392 (2018). https://doi.org/10.1007/s40840-016-0307-5
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DOI: https://doi.org/10.1007/s40840-016-0307-5