A construction of -spaces and related Banach spacesand related Banach spaces Academic Article uri icon


  • Let >1. We prove that every separable Banach space E can be embedded isometrically into a separable -space X such that X/E has the RNP and the Schur property. This generalizes a result in [2]. Various choices of E allow us to answer several questions raised in the literature. In particular, taking E = 2, we obtain a -space X with the RNP such that the projective tensor product {Mathematical expression} contains c 0 and hence fails the RNP. Taking E=L 1, we obtain a -space failing the RNP but nevertheless not containing c 0. 1983 Sociedade Brasileira de Matemtica.

published proceedings

  • Bulletin of the Brazilian Mathematical Society, New Series

author list (cited authors)

  • Bourgain, J., & Pisier, G.

citation count

  • 38

complete list of authors

  • Bourgain, Jean||Pisier, Gilles

publication date

  • January 1983