Article - preprint
nilpotent operators of order two, Hilbert space operators, Toeplitz operator
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.
© 2012 Stephan Ramon Garcia, Bob Lutz, and Dan Timotin
Garcia, Stephan Ramon; Lutz, Bob '13; and Timotin, D., "Two Remarks about Nilpotent Operators of Order Two" (2012). Pomona Faculty Publications and Research. 203.
Pre-print from arXiv: http://arxiv.org/abs/1206.5523
Final publication can be found at:
Garcia, S.R., Lutz, B., Timotin, D., Two remarks about nilpotent operators of order two, Proc. Amer. Math. Soc. (in press).