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 $l_p$ Math. Nachr. 281, 2008, 412423; 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 nonpnuclear operators with pnuclear second adjoints" (Math. Nachr. 109(1982), 125134) and "Approximation of operators in Banach spaces" (Application of functional analysis in the approximation theory (KGU, Kalinin), 1985, 128142) by Reinov O.I. have been appeared in 1982 and in 1985 respectively.
 Publication:

arXiv eprints
 Pub Date:
 February 2010
 arXiv:
 arXiv:1003.0085
 Bibcode:
 2010arXiv1003.0085R
 Keywords:

 Mathematics  Functional Analysis;
 46B28
 EPrint:
 LATeX, English (4 pp.). Added some notations and a few remarks. Misprints are corrected.