The property of smallness up to a complemented Banach subspace

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.


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Citation Formats
T. Abdeljawad and M. H. Yurdakul, “The property of smallness up to a complemented Banach subspace,” PUBLICATIONES MATHEMATICAE-DEBRECEN, pp. 415–425, 2004, Accessed: 00, 2020. [Online]. Available: