Student Co-author

Pomona Undergraduate

Document Type

Article - preprint

Department

Mathematics (Pomona)

Publication Date

2012

Keywords

nilpotent operators of order two, Hilbert space operators, Toeplitz operator

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.

Comments

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).

Rights Information

© 2012 Stephan Ramon Garcia, Bob Lutz, and Dan Timotin

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Share

COinS