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Neha Hotwani

Publications and source records attributed to Neha Hotwani.

5 recordsLinked to original sources
arXiv2026

Vector valued continuous function spaces as $C^\ast$-algebras

Let \(\Omega\) be a compact Hausdorff space, and let \(\cA\) be a unital \(C^*\)-algebra. In this study, we continue our examination of the comparison between \(C^*\)-extreme points and linear extremal structures of the unit ball, in the vector-valued \(C^*\)-algebra \(C(\Omega, \cA)\), building upon the work initiated in \cite{HR}. We first enlarge the class of $C^\ast$-algebras in which a $ C^\ast$-extreme point is an extreme point. We demonstrate that if \(\cA\) has a faithful tracial state, then any \(C^*\)-extreme point of the unit ball \(C(\Omega, \cA)_1\) is a unitary. Additionally, we identify a classes of \(C^*\)-algebras where the concepts of \(C^*\)-extreme and pointwise \(C^*\)-extreme points in \(C(\Omega, \cA)_1\) coincide. We show this holds if a von Neumann algebra has a separable predual with the Radon-Nikod\'ym property.

math.OA↗
arXiv2026

Weakly Compact Operators Whose Adjoints Preserve $C^*$-Structure

Let $\Omega$ be a compact Hausdorff space and $X$ be a complex Banach space such that $X^{**}$ is isometric to a $C^*$-algebra. Let $\mathcal{W}(X^*, C(\Omega))$ denote the space of weakly compact operators. In this article, we show that the collection of operators $T$ in $\mathcal{W}(X^*, C(\Omega))$ such that $T^*$ maps linear extreme points of the unit ball of $C(\Omega)^*$ to $C^*$-extreme points of $X^{**}$ is a uniformly strongly extreme set. We also investigate this phenomenon when $X^{**}$ is isometric to a space of all operators on a Banach space.

math.FA↗
arXiv2025

Geometric Aspects of $C^*$-Extreme Points

We provide a characterization of the $C^*$-extreme points of the closed unit ball of a von Neumann algebra and demonstrate that $C^*$-extremality is equivalent to both linear extremality and strong extremality. As an application, we characterize certain classes of von Neumann algebras in terms of their $C^*$-extreme points.

math.OA↗
arXiv2024

C*-extreme entanglement breaking maps on operator systems

Let $\mathcal E$ denote the set of all unital entanglement breaking (UEB) linear maps defined on an operator system $\mathcal S \subset M_d$ and, mapping into $M_n$. As it turns out, the set $\mathcal E$ is not only convex in the classical sense but also in a quantum sense, namely it is $C^*$-convex. The main objective of this article is to describe the $C^*$-extreme points of this set $\mathcal E$. By observing that every EB map defined on the operator system $\mathcal S$ dilates to a positive map with commutative range and also extends to an EB map on $M_d$, we show that the $C^*$-extreme points of the set $\mathcal E$ are precisely the UEB maps that are maximal in the sense of Arveson (\cite{A} and \cite{A69}) and that they are also exactly the linear extreme points of the set $\mathcal E$ with commutative range. We also determine their explicit structure, thereby obtaining operator system generalizations of the analogous structure theorem and the Krein-Milman type theorem given in \cite{BDMS}. As a consequence, we show that $C^*$-extreme (UEB) maps in $\mathcal E$ extend to $C^*$-extreme UEB maps on the full algebra. Finally, we obtain an improved version of the main result in \cite{BDMS}, which contains various characterizations of $C^*$-extreme UEB maps between the algebras $M_d$ and $M_n$.

math.OA↗