The approximation property does not imply the bounded approximation property Academic Article uri icon


  • There is a Banach space which has the approximation property but fails the bounded approximation property. The space can be chosen to have separable conjugate, hence there is a nonnuclear operator on the space which has nuclear adjoint. This latter result solves a problem of Grothendieck [2]. 1973 American Mathematical Society.

published proceedings

  • Proceedings of the American Mathematical Society

altmetric score

  • 3

author list (cited authors)

  • Figiel, T., & Johnson, W. B.

citation count

  • 50

complete list of authors

  • Figiel, T||Johnson, WB

publication date

  • January 1973