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Full-Text Articles in Physical Sciences and Mathematics
Interpolation And Complex Symmetry, Stephan Ramon Garcia, Mihai Putinar
Interpolation And Complex Symmetry, Stephan Ramon Garcia, Mihai Putinar
Pomona Faculty Publications and Research
In a separable complex Hilbert space endowed with an isometric conjugate-linear involution, we study sequences orthonormal with respect to an associated bilinear form. Properties of such sequences are measured by a positive, possibly unbounded angle operator which is formally orthogonal as a matrix. Although developed in an abstract setting, this framework is relevant to a variety of eigenvector interpolation problems arising in function theory and in the study of differential operators.
Complex Symmetric Operators And Applications Ii, Stephan Ramon Garcia, Mihai Putinar
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 …