The property of smallness up to a complemented Banach subspace

Abdeljawad T., Yurdakul M.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.64, pp.415-425, 2004 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64
  • Publication Date: 2004
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.415-425


This article investigates locally convex spaces which satisfy the property of smallness up to a complemented Banach subspace, the SCBS property, which was introduced by Djakov, Terzioglu, Yurdakul and Zahariuta. It is proved that a bounded perturbation of an automorphism on a complete barrelled locally convex, space with the SCBS is stable up to a Banach subspace. New examples are given, and the relation of the SCBS with the quasinormability is analyzed. It is proved that the Frechet space l(p+) does not satisfy the SCBS, therefore this property is not inherited by subspaces or separated quotients.