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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 of Hilbert space operators, the 'commuting dilation constant' is the smallest number such that the operators of 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 -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 operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.