An overview of semi-continuity results on the spectral radius and positivity

Our aim is to provide a novelly comprehensive and unifying approach to showing the continuous dependence of the spectral radius of compact linear operators defined on Banach spaces (with specific attention to positive operators defined on normal Banach spaces) and emphasizing that the upper semi-continuity generally holds unlike the lower semi-continuity. © 2007 Elsevier Inc. All rights reserved