Abdeljawad, ThabetYurdakul, M.2021-12-142021-12-142004-04Abdeljawad, Thabet; Yurdakul, M. (2004). "The property of smallness up to a complemented Banach subspace", Publicationes Mathematicae-Debrecen, Vol. 64, No. 3-4, pp. 415-425.0033-3883http://hdl.handle.net/20.500.12416/4964This 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.enginfo:eu-repo/semantics/closedAccessThe SCBS PropertyThe Conditions (QN)(AN)l-KotheSpacesThe Space l(p)+Bounded Factorization PropertyDouady's LemmaComplemented Banach Subspacesarticle643-4415425