Banach spaces without approximation properties of type p

  title={Banach spaces without approximation properties of type p},
  author={Oleg I. Reinov and Qaisar Latif},
  journal={Mathematical Notes},
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. 


Approximation of operators in Banach spaces
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
Compact operators which factor through subspaces of lp
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
Approximation properties of order p and the existence of non-p-nuclear operators with p-nuclear second adjoints
Disappearance of tensor elements in the scale of p-nuclear operators, Theory of operators and theory of functions (LGU
  • 1983
Operator ideals, North-Holland
  • Deutscher Verlag der Wiss., Berlin,
  • 1978