The property of smallness up to a complemented Banach subspace

Date

2004-04-01

Author

Abdeljawad, T
Yurdakul, Murat Hayrettin

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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.

Subject Keywords

The SCBS property, the conditions (QN), (AN), l-Kothe, Spaces, The spacepace l(p)+, Bounded factorization property, Douady's lemma, Complemented Banach subspaces l(p)+, Bounded factorization property, Douady's lemma, Complemented Banach subspaces l(p)+

URI

https://hdl.handle.net/11511/55728

Journal

PUBLICATIONES MATHEMATICAE-DEBRECEN

Collections

Graduate School of Natural and Applied Sciences, Article

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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: https://hdl.handle.net/11511/55728.