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The property of smallness up to a complemented Banach subspace
Date
2004-04-01
Author
Abdeljawad, T
Yurdakul, Murat Hayrettin
Metadata
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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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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.