Photo from archive.org
For a positive integer m, a bounded linear operator T on a Hilbert space $$\mathbb {H}$$H is called an (A, m)-isometry, if $$\Theta ^{(m)}_{A}(T) =\sum _{k=0}^{m}(-1)^{m-k}{m\atopwithdelims ()k}T^{*k}AT^{k}=0$$ΘA(m)(T)=∑k=0m(-1)m-kmkT∗kATk=0, where A is a… Click to show full abstract
For a positive integer m, a bounded linear operator T on a Hilbert space $$\mathbb {H}$$H is called an (A, m)-isometry, if $$\Theta ^{(m)}_{A}(T) =\sum _{k=0}^{m}(-1)^{m-k}{m\atopwithdelims ()k}T^{*k}AT^{k}=0$$ΘA(m)(T)=∑k=0m(-1)m-kmkT∗kATk=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 $$\Theta ^{(2)}_{A}(T)\le 0$$ΘA(2)(T)≤0).
Journal Title: Bulletin of the Malaysian Mathematical Sciences Society
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!