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Daily Overview |
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Al2: Algebra Location: M627 Session Chair: Peter Fiebig Session Chair: Nikita Geldhauser | |
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Matrix and Operator K-Positivity Preserver University of Konstanz, Germany A positivity preserving operator $T: \mathbb{R}[x_1, \dots, x_n] \to \mathbb{R}[x_1, \dots, x_n]$ on polynomials is a linear operators such that positive polynomials on some closed set $K \subseteq \mathbb{R}^n$ are mapped to positive polynomials on $K$ again. These positivity preservers on polynomials have been characterized by Borcea's Theorem which links positivity to moment sequences. We will present Borcea's Theorem and some of its applications, as well as a generalization of Borcea's Theorem to operator polynomials $B(\mathcal{H})_h \otimes \mathbb{R}[x_1, \dots, x_n]$ which are real polynomials where the coefficients are bounded linear self-adjoint operators on some Hilbert space $\mathcal{H}$. The operator polynomial case also includes matrix polynomials with Hermitian matrices as coefficients. | |
