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

Emel'yanov E.

SIBERIAN MATHEMATICAL JOURNAL, cilt.44, sa.5, ss.793-796, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 5
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1023/a:1025976401206
  • Dergi Adı: SIBERIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.793-796
  • Anahtar Kelimeler: C-0-semigroup, invariant subspace of a semi-roup, almost periodic semigroup, BANACH-SPACES
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.