Marcel Scherer

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20232026

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5 papers · 1 filter

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.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…

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

The Hyperrigidity Conjecture for compact convex sets in R2

Spectra of typical Hilbert space operators

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