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arXiv · 0907.4486

Complex symmetric partial isometries

Stephan Ramon Garcia·Warren R. Wogen
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Abstract

An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric.

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Stephan Ramon Garcia, Warren R. Wogen. 2009-07-26. Complex symmetric partial isometries. https://doi.org/10.1016/j.jfa.2009.04.005

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