Some conditions for a co-semigroup to be asymptotically finite-dimensional


Emel'yanov E.

SIBERIAN MATHEMATICAL JOURNAL, vol.44, no.5, pp.793-796, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 5
  • Publication Date: 2003
  • Doi Number: 10.1023/a:1025976401206
  • Title of Journal : SIBERIAN MATHEMATICAL JOURNAL
  • Page Numbers: pp.793-796
  • Keywords: C-0-semigroup, invariant subspace of a semi-roup, almost periodic semigroup, BANACH-SPACES

Abstract

We study the class of bounded C-0-semigroups T = (T-t)(tgreater than or equal to0) on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X-0(T) < infinity, where X-0(T) := {x is an element of X: lim(t-->infinity)parallel toT(t)xparallel to = 0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.