Marcel Scherer

activity

20232026

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4 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.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…