On (N, )-pseudospectra of operators on Banach spaces

In this paper we extend the concept of the (N, )-pseudospectra of Hansen to the case of bounded linear operators on Banach spaces and prove several relations to the usual spectrum. We particularly discuss the approximation by rectangular finite sections and the impact of the fundamental result of Shargorodsky on “jumping” pseudospectra. © 2012 Elsevier Inc. All rights reserved.