Complex symmetric partial isometries

Stephan Ramon Garcia; Warren R. Wogen

doi:10.1016/j.jfa.2009.04.005

Complex symmetric partial isometries

Functional Analysis 2009-07-28 v1 Operator Algebras

Authors: 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.

Keywords

operator theory on hilbert spaces operator theory numerical range

Cite

@article{arxiv.0907.4486,
  title  = {Complex symmetric partial isometries},
  author = {Stephan Ramon Garcia and Warren R. Wogen},
  journal= {arXiv preprint arXiv:0907.4486},
  year   = {2009}
}

Comments

9 pages

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