The property of smallness up to a complemented Banach subspace


Abdeljawad T., Yurdakul M.

PUBLICATIONES MATHEMATICAE-DEBRECEN, cilt.64, ss.415-425, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 64
  • Basım Tarihi: 2004
  • Dergi Adı: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Sayfa Sayıları: ss.415-425

Özet

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.