Banach spaces without approximation properties of type p

The main purpose of this note is to show that the question posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which factor through subspaces of \(l_p\) Math. Nachr. 281, 2008, 412-423; see the very end of that paper) has a negative answer, and that the answer was known, essential...

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Bibliographic Details
Published in:arXiv.org 2010-04
Main Authors: Reinov, Oleg, Latif, Qaisar
Format: Article
Language:English
Subjects:
Adjoints
Approximation
Banach spaces
Error analysis
Functional analysis
Mathematical analysis
Operators (mathematics)
Subspaces
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Summary:The main purpose of this note is to show that the question posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which factor through subspaces of \(l_p\) Math. Nachr. 281, 2008, 412-423; see the very end of that paper) has a negative answer, and that the answer was known, essentially, in 1985 after the papers "Approximation properties of order p and the existence of non-p-nuclear operators with p-nuclear second adjoints" (Math. Nachr. 109(1982), 125-134) and "Approximation of operators in Banach spaces" (Application of functional analysis in the approximation theory (KGU, Kalinin), 1985, 128-142) by Reinov O.I. have been appeared in 1982 and in 1985 respectively.
ISSN:2331-8422