Universal Jamison spaces and Jamison sequences for C-0-semigroups

作者：Devinck Vincent^*

来源：Studia Mathematica, 2013, 214(1): 77-99.

DOI：10.4064/sm214-1-5

• partially power-bounded operators
• unimodular point spectrum
• Jamison sequences

An increasing sequence (n(k))(k >= 0) of positive integers is said to be a Jamison sequence if for every separable complex Banach space X and every T is an element of B(X) which is partially power-bounded with respect to (n(k))(k >= 0), the set sigma(p)(T) boolean AND T is at most countable. We prove that for every separable infinite-dimensional complex Banach space X which admits an unconditional Schauder decomposition, and for any sequence (n(k))(k >= 0) which is not a Jamison sequence, there exists T is an element of B(X) which is partially power-bounded with respect to (n(k))k >= 0 and has the set sigma(p)(T) boolean AND T uncountable. We also investigate the notion of Jamison sequences for C-0-semigroups and we give an arithmetic characterization of such sequences.

• 出版日期2013