Student Co-author

Pomona Undergraduate

Document Type

Article - preprint


Mathematics (Pomona)

Publication Date



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.


Pre-print from arXiv:

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

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