Point spectra of partially power-bounded operators

Abstract: Let T be an operator on a separable Banach space, and denote by its point spectrum. We answer a question left open in (Israel J. Math. 146 (2005) 93–110) by showing that it is possible that be uncountable, yet . We further investigate the relationship between the growth of sequences such that and the possible size of . Analogous results are also derived for continuous operator semigroups . [Copyright &y& Elsevier]