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arXiv · 1206.5523

Two remarks about nilpotent operators of order two

Stephan Ramon Garcia·Bob Lutz·Dan Timotin
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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.

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Stephan Ramon Garcia, Bob Lutz, Dan Timotin. 2012-07-15. Two remarks about nilpotent operators of order two. https://arxiv.org/abs/1206.5523

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