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Linda Patton (Cal Poly San Luis Obispo)5/18/26, 11:00 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
Using results from Brown-Halmos, Klein (1972) described the numerical range of a general Toeplitz operator on $H^2(\mathbb{D})$. In particular, the numerical range of a Toeplitz operator $T_p$ with polynomial symbol $p$ is the convex hull of the image of the unit disk under $p$. By analyzing $p(\mathbb{T})$ and its relationship to the Kippenhahn curve of a matrix, we provide conditions under...
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Nancy Menzelthe (University of Nevada, Reno)5/18/26, 11:25 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
Given $1\le k\le n$, the $k$-numerical range of $A\in \mathbb{C}_{n\times n}$ is defined by
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$$ W_k(A): = \left\{ \sum_{i=1}^k x_i^*Ax_i: x_1, \dots, x_k\ \mbox {orthonormal vectors in } \mathbb{C}^n\right\}\subset \mathbb{C}. $$ Motivated by Davis' intuitive explanation of the Elliptical Range Theorem, we introduce two notions of multiplicity for points in $W_k(A)$, namely wedge... -
Edward Poon5/18/26, 11:50 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
The spatial numerical range of an operator $T$ on a normed space $(\mathcal{X}, \| \cdot \|)$ is the set $$W(T) = \{f(Tx) : x \in \mathcal{X}, f \in \mathcal{X}^*, \|x\| = \|f\|^d = f(x) = 1\};$$ when $| \cdot |$ is induced by an inner product this coincides with the classical numerical range. We investigate some properties of the spatial numerical range.
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Prof. Shmuel Friedland (University of Illinois Chicago)5/20/26, 10:45 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
In this talk we survey some recent results on entanglement and separability of general, symmetric (bosons), skew-symmetric (fermions) tensors, and their computability. All these results are related to corresponding numerical radii. This talk is based on the arXiv preprint
S. Friedland, Tensors, entanglement, separability, and their complexity, arXiv:2509.21639, 2025.
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Dr Tejbir Lohan (Indian Statistical Institute, Delhi Centre, India)5/20/26, 11:10 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
Linear preserver problems study linear maps on matrix spaces that leave certain functions, subsets, or relations invariant, whereas matrix decomposition problems focus on expressing matrices as products of matrices with prescribed structural properties. An element of the algebra $M_n(\mathbb{F})$ of $n \times n$ matrices over a field $\mathbb{F}$ is called an involution if its square equals...
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Kennett Dela Rosa (University of the Philippines Diliman)5/20/26, 11:35 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
This study considers some problems involving the $k$-numerical range. Following the idea of the zero-dilation index, the notion of the zero-trace index is introduced, which is defined as the largest zero-trace compression of a matrix. Alternative characterization of the zero-trace index is given, and zero-trace indices of certain classes of matrices are identified. The study also considers...
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Rute Lemos (CIDMA, University of Aveiro, Portugal)5/21/26, 11:00 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
The higher rank numerical range is investigated for 2-by-2 block matrices with associated Kippenhahn curves consisting of ellipses and eventually points. As a consequence, elliptical higher rank numerical range results are derived in a unified way, using an approach developed by Spitkovsky et al.
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Brooke Randell (UCSC)5/21/26, 11:25 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
In 2022, Hwa-Long Gau and Pei Yuan Wu discussed the numerical range of various Hankel matrices with an emphasis on which subsets of the complex plane are attainable. We will be discussing as well as expanding upon these results when the Hankel matrices are positive and Hermitian.
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Daisuke Hirota (National Institute of Technology, Tsuruoka College)5/21/26, 11:50 AMNumerical Ranges and Numerical RadiiMinisymposium Talk
The Cauchy functional equation plays a fundamental role in the study of additive and linear structures arising from numerical and norm-related information in functional analysis. In this talk, we investigate preserver problems on positive cones of commutative C$^{*}$-algebras, where a norm identity of Fischer--Muszély type, arising from the Cauchy functional equation, determines the underlying...
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