pith. sign in

arxiv: 0907.3761 · v1 · submitted 2009-07-22 · 🧮 math.FA · math.OA

Some new classes of complex symmetric operators

classification 🧮 math.FA math.OA
keywords complexsymmetricoperatorsclassesoperatorabstractalgebraicattempt
0
0 comments X
read the original abstract

We say that 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 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 $(\dim \ker T, \dim \ker T^*)$.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.