Banach spaces without approximation properties of type p

@article{Reinov2010BanachSW,
title={Banach spaces without approximation properties of type p},
author={Oleg I. Reinov and Qaisar Latif},
journal={Mathematical Notes},
year={2010},
volume={88},
pages={559-562}
}

The main purpose of this note is to show that the question posed in the paper [1] of D. P. Sinha D. P. and A. K. Karn (see the very end of that paper) has a negative answer, and that the answer could have been obtained, essentially, in 1985 after the papers [2], [3] by the author appeared in 1982 and 1985, respectively.

It is a translation of an old paper of mine. We describe the topology tau_p in the space Pi_p(Y,X), for which the closures of convex sets in tau_p and in *-weak topology of the space Pi_p(Y,X) are… Expand

Let 1 ≤ p ≤ ∞. A subset K of a Banach space X is said to be relatively p -compact if there is an 〈xn〉 ∈ lsp (X) such that for every k ∈ K there is an 〈αn〉 ∈ lp ′ such that k = σ∞n=1αnxn. A linear… Expand