Year: 2026
Type: preprint
Abstract: We show that the spectral radius introduced by Shalit and Shamovich uniquely determines the underlying operator space structure: If E_1 and E_2 are operator space structures on C^d such that the corresponding spectral radii ρ_{E_1} and ρ_{E_2} 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.
Source: arXiv (Cornell University)
Author: Tornes, Maximilian
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216456852