Formulae for joint spectral radii of sets of operators (Q2773407)

The formula \(\rho(M)=\max\{\rho_\chi(M), r(M)\}\) is proved for precompact sets \(M\) of weakly compact operators on a Banach space. Here \(\rho(M)\) is the joint spectral radius (the Rota-Strang radius), \(\rho_\chi(M)\) is the Hausdorff spectral radius (connected with the Hausdorff measure of noncompactness) and \(r(M)\) is the Berger-Wang radius. The work is a further development of the ideas of earlier papers, namely \textit{G.-C. Rota} and \textit{W. G. Strang} [Nederl. Akad. Wet., Proc., Ser. A 63, 379-381 (1960; Zbl 0095.09701)] and \textit{M. A. Berger} and \textit{Y. Wang} [Linear Algebra Appl. 166, 21-27 (1992; Zbl 0818.15006)].