We extend and refine the approach of  concerning essential selfadjointness (normality) of a densely defined operator subject to some domination condition involving the first or the second commutator.
The aim of this paper is to analyze a “support-free” version of the Riesz–Haviland theorem proved recently by the present authors, which characterizes truncations of the complex moment problem via positivity condition on appropriate families of polynomials in z and z¯. The attention is focused on modifications of the positivity condition as well as the assumption on admissible truncations. The former...
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
Orthogonality of polynomials in several variables with respect to a positive Borel measure supported on an algebraic set is the main theme of this paper. As a step towards this goal quasi-orthogonality with respect to a non-zero Hermitian linear functional is studied in detail; this occupies a substantial part of the paper. Therefore necessary and sufficient conditions for quasi-orthogonality in terms...
The Newman-Shapiro Isometry Theorem is proved in the case of Segal-Bargmann spaces of entire vector-valued functions (i.e. summable with respect to the Gaussian measure on ℂⁿ). The theorem is applied to find the adjoint of an unbounded Toeplitz operator with φ being an operator-valued exponential polynomial.
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