Isometric properties of elementary operators
We consider the elementary operator L, acting on the Hilbert-Schmidt Class C2 (H), given by L (T) = ATB, with A and B bounded operators on H. We establish necessary and sufficient conditions on A and B for L to be a 2-isometry or a 3-isometry. We derive sufficient conditions for L to be an n-isometry. We also give several illustrative examples involving the weighted shift operator on l2 and the multiplication operator on the Dirichlet space. © 2009 Elsevier Inc. All rights reserved.
Linear Algebra and Its Applications
Botelho, F., & Jamison, J. (2010). Isometric properties of elementary operators. Linear Algebra and Its Applications, 432 (1), 357-365. https://doi.org/10.1016/j.laa.2009.08.013