Complex symmetric partial isometries

Abstract

An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T=C{T}^{\ast }C$. 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 $\le 4$ is complex symmetric.

9 pages

References in corpus (1)

• Unitary equivalence to a complex symmetric matrix: geometric criteria

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• Unitary equivalence to a complex symmetric matrix: low dimensions
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• Some new classes of complex symmetric operators