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A Spectral Radius for Matrices over an Operator Space

For each operator space structure E on C^d, a spectral radius function on tuples of operators whose value is below one exactly when the tuple is jointly similar, via a single structure-respecting invertible scalar matrix, to a tuple in the open unit ball of M_n(E). It unifies and sharpens the joint spectral radii of Bunce-Popescu and Rota-Strang and characterizes the domain of a noncommutative rational function through the dual operator space.

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A SPECTRAL RADIUS FOR MATRICES OVER AN OPERATOR SPACE ORR MOSHE SHALIT AND ELI SHAMOVICH Abstract.

For every operator space structure E on C^d, the authors associate a spectral radius function rho_E defined on d-tuples of operators, generalizing the classical spectral radius that detects when a si…