Complex symmetric operators, interpolation, self-adjoint extension, Takagi factorization, shift operators, inner functions, Darlington synthesis, Clark perturbations, Jordan operators, Volterra operators
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.
© 2005 American Mathematical Society
Garcia, S.R., Putinar, M., Complex symmetric operators and applications, Trans. Amer. Math. Soc. 358 (2006), 1285–1315. MR2187654 (2006j:47036)