Complex symmetric partial isometries

Details Complex symmetric partial isometries Complex symmetric partial isometries

2009-07-26

arxiv.org/abs/0907.4486v1

J. Funct. Analysis 257 (2009), 1251-1260

Mathematics

Functional Analysis

9 pages

Scientific paper

10.1016/j.jfa.2009.04.005

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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