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New Classes of Complex Symmetric Operators
by
Stephan Ramon Garcia
Pomona College
Coauthors: Warren R. Wogen (U.N.C. Chapel Hill)
We say that an operator T ∈ B(H) is complex symmetric if there exists a conjugate-linear, isometric involution C:H→H so that T = CT*C. It is known that the class of complex symmetric operators is large, containing all normal operators, the Volterra integration operator, compressed Toeplitz operators (including the compressed shift and Aleksandrov-Clark operators), and operators induced by Hankel and Toeplitz matrices, among others.
In this talk (joint work with W. Wogen), we discuss several recent additions to this family. In particular, we explain why binormal operators, operators which 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 happen to be complex symmetric. Additionally, we describe all complex symmetric partial isometries and highlight some surprises that occur in low-dimensions.
This talk will be accessible to any analyst.
Date received: January 30, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-26.