Some new classes of complex symmetric operators
Functional Analysis
2009-07-23 v1 Operator Algebras
Abstract
We say that an operator is complex symmetric if there exists a conjugate-linear, isometric involution so that . We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data .
Cite
@article{arxiv.0907.3761,
title = {Some new classes of complex symmetric operators},
author = {Stephan Ramon Garcia and Warren R. Wogen},
journal= {arXiv preprint arXiv:0907.3761},
year = {2009}
}
Comments
13 pages, to appear in Transactions of the AMS