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Complex Symmetric Operators And Applications, Stephan Ramon Garcia, Mihai Putinar
Complex Symmetric Operators And Applications, Stephan Ramon Garcia, Mihai Putinar
Pomona Faculty Publications and Research
We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.