Complex Symmetric Operators and Applications Ii
نویسندگان
چکیده
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-selfadjoint operators, originally introduced by Glazman. In this context, it provides a method for estimating the norms of the resolvents of certain unbounded operators.
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