Banach spaces without approximation properties of type p
Abstract
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 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.
Cite
@article{arxiv.1003.0085,
title = {Banach spaces without approximation properties of type p},
author = {Oleg Reinov and Qaisar Latif},
journal= {arXiv preprint arXiv:1003.0085},
year = {2010}
}
Comments
LATeX, English (4 pp.). Added some notations and a few remarks. Misprints are corrected.