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Complex Symmetric Operators And Applications Ii, Stephan Ramon Garcia, Mihai Putinar

Pomona Faculty Publications and Research

A bounded linear operator T on a complex Hilbert space H is called complex symmetric if T = CT*C, where C is a conjugation (an isometric, antilinear involution of H). We prove that T = CJ|T|, where J is an auxiliary conjugation commuting with |T| = √{T*T). We consider numerous examples, including the Poincaré-Neumann singular integral (bounded) operator and the Jordan model operator (compressed shift). The decomposition T = CJ|T| also extends to the class of unbounded C-self adjoint operators, originally introduced by Glazman. In this context, it provides a method for estimating the norms …