Formulae for joint spectral radii of sets of operators
Volume 149 / 2002
Studia Mathematica 149 (2002), 23-37
MSC: Primary 47A13, 47D03, 47A30.
DOI: 10.4064/sm149-1-2
Abstract
The formula $\varrho(M)=\max\{\varrho_{\chi}(M),r(M)\}$ is proved for precompact sets $M$ of weakly compact operators on a Banach space. Here $\varrho(M)$ is the joint spectral radius (the Rota–Strang radius), $\varrho_{\chi}(M)$ is the Hausdorff spectral radius (connected with the Hausdorff measure of noncompactness) and $r(M)$ is the Berger–Wang radius.
