Two remarks about nilpotent operators of order two
Functional Analysis
2012-07-17 v2 Complex Variables
Operator Algebras
Abstract
We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a complex symmetric operator. In fact, we prove that this property characterizes nilpotents of order two among all nonzero bounded operators. Second, we establish that every nilpotent of order two is unitarily equivalent to a truncated Toeplitz operator.
Cite
@article{arxiv.1206.5523,
title = {Two remarks about nilpotent operators of order two},
author = {Stephan Ramon Garcia and Bob Lutz and Dan Timotin},
journal= {arXiv preprint arXiv:1206.5523},
year = {2012}
}
Comments
7 pages. To appear in Proceedings of the AMS