The property of smallness up to a complemented Banach subspace
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Date
2004
Authors
Yurdakul, M.
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Abstract
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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The SCBS Property, The Conditions (QN), (AN), l-Kothe, Spaces, The Space l(p)+, Bounded Factorization Property, Douady's Lemma, Complemented Banach Subspaces
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Citation
Abdeljawad, 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.
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Publicationes Mathematicae-Debrecen
Volume
64
Issue
3-4
Start Page
415
End Page
425