On the Shalit-Shamovich Spectral Radius
Maximilian Tornes
Abstract
We show that the spectral radius introduced by Shalit and Shamovich uniquely determines the underlying operator space structure: If E1 and E2 are operator space structures on Cd such that the corresponding spectral radii ρE1 and ρE2 agree on every d-tuple of operators, then the identity map is completely isometric. This answers a question of Scherer, Shalit and Shamovich. Moreover, we obtain an analogous result for the minimal spectral radii, and showcase an application to the completely bounded isomorphism problem for algebras of bounded non-commutative functions on operator space unit balls.
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