The spectral radius of an element of a -Banach algebra can be calculated as the supremum of the spectral radii in the fibres. As a consequence, calculations in K-theory for such algebras can potentially be carried out fibrewise.
Cite this article
Walther Paravicini, The spectral radius in -Banach algebras. J. Noncommut. Geom. 7 (2013), no. 1, pp. 135–147