Two‐Sided Bounds for the Spectral Radius of a Positive Linear Map
Ivo Marek, Karel Žitný · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1984
Abstract In this paper it is shown that the spectral radius of a cone preserving linear bounded map of Banach space (not necessarily finite‐dimensional) can be approximated both from below and above by spectral radii of two n X n matrices with non‐negative entries. The results obtained extend some known results, in particular, the Collatz's “classical” Einschließungssatz and E. Deutsch's recent two‐sided spectral bound theorem for partitioned matrices.