Marcel Scherer

activity

20232026

collaborators

10 papers

math.OA2026

A Three-Dimensional Operator System without the Smith--Ward Property

Marcel Scherer

Harris recently showed that a non-liftable injective representation into the Calkin algebra gives explicit four-dimensional operator systems in the Calkin algebra without the lifti…

math.OA2026

On the spectral radius of operator tuples

Marcel Scherer, Orr Shalit, Eli Shamovich

In recent work, Shalit and Shamovich associated to every operator space structure $E$ on $C^{d}$ a spectral radius function $ρ_{E}$ on $d$ -tuples of oper…

math.OA2026

The Hyperrigidity Conjecture for Spectrahedra

Marcel Scherer

We show that if K is a compact spectrahedron whose set of extreme points is closed, then the operator system of continuous affine functions on K is hyperrigid in the C*-algebra C(e…

math.OA2026

A C*-cover lattice dichotomy

Adam Humeniuk, Christopher Ramsey, Marcel Scherer

In this paper, we show that the lattice of C*-covers of a non-selfadjoint operator algebra is either one point or uncountable. We prove that there are non-selfadjoint operator alge…

math.FA2025

Empirical bounds for commuting dilations of free unitaries and the universal commuting dilation constant

Malte Gerhold, Marcel Scherer, Orr Shalit

For a tuple $T$ of Hilbert space operators, the 'commuting dilation constant' is the smallest number $c$ such that the operators of $T$ are a simultaneous compression of commuting…

math.FA2025

The SOT-closure of the set of 2-isometries

Marcel Scherer

We show that the set of $2$ -isometries on an infinite-dimensional Hilbert space is not closed in the strong operator topology. In fact, we prove that its SOT-closure coincides with…

math.FA2025

A Finite Dimensional Counterexample for Arveson's Hyperrigidity Conjecture

Marcel Scherer

We construct an operator system generated by $4$ operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.

math.OA2025

Hyperrigidity III

Paweł Pietrzycki, Marcel Scherer, Jan Stochel

In this paper, we study hyperrigidity for $C^{*}$ -algebras. We will show that hyperrigidity can be expressed solely in terms of representations, without the need to involve general u…

math.FA2024

The Hyperrigidity Conjecture for compact convex sets in $R^{2}$

Marcel Scherer

We prove that for every compact, convex subset $K \subset R^{2}$ the operator system $A (K)$ , consisting of all continuous affine functions on $K$ , is hyperrigid in the C*-alge…

math.FA2023

Spectra of typical Hilbert space operators

Marcel Scherer

Let $B (H)$ be the bounded, linear operators on a separable Hilbert space equipped with the norm topology. A property is called typical if the set of operators fulfilling…

A Three-Dimensional Operator System without the Smith--Ward Property

On the spectral radius of operator tuples

The Hyperrigidity Conjecture for Spectrahedra

A C*-cover lattice dichotomy

Empirical bounds for commuting dilations of free unitaries and the universal commuting dilation constant

The SOT-closure of the set of 2-isometries

A Finite Dimensional Counterexample for Arveson's Hyperrigidity Conjecture

Hyperrigidity III

The Hyperrigidity Conjecture for compact convex sets in R2

Spectra of typical Hilbert space operators

The Hyperrigidity Conjecture for compact convex sets in $R^{2}$