Point spectra of partially power-bounded operators.

Journal article, 2006

Let T be an operator on a separable Banach space, and denote by σ p (T) its point spectrum. We answer a question left open in (Israel J. Math. 146 (2005) 93-110) by showing that it is possible that σ p (T) ∩ T be uncountable, yet ∥T n ∥ → ∞. We further investigate the relationship between the growth of sequences (n k ) such that sup k ∥T nk ∥ < ∞ and the possible size of σ p (T) ∩ T. Analogous results are also derived for continous operator semigroups (T t ) t≥0 . © 2005 Elsevier Inc. All rights reserved.