## Pomona Faculty Publications and Research

#### Title

Complex Symmetric Partial Isometries

#### Document Type

Article - preprint

#### Department

Mathematics (Pomona)

2009

#### Keywords

Complex symmetric operator, Isometry, Partial isometry

#### 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.

Pre-print from http://arxiv.org/abs/0907.4486

Final publication can be found at:

Stephan Ramon Garcia, Warren R. Wogen, Complex symmetric partial isometries, Journal of Functional Analysis, Volume 257, Issue 4, 15 August 2009, Pages 1251-1260, ISSN 0022-1236, http://dx.doi.org/10.1016/j.jfa.2009.04.005. (http://www.sciencedirect.com/science/article/pii/S0022123609001694)