The optimality of James's distortion theorems Academic Article uri icon

abstract

  • A renorming of , explored here in detail, shows that the copies of il produced in the proof of the Kadec-Pelczyriski theorem inside nonreflexive subspaces of L1[0,1] cannot be produced inside general nonreflexive spaces that contain copies of t. Put differently, James's distortion theorem producing one-plus-epsilon-isomorphic copies of inside any isomorphic copy of is, in a certain sense, optimal. A similar renorming of c0 shows that James's distortion theorem for c0 is likewise optimal. 1997 American Mathematical Society.

published proceedings

  • PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Dowling, P. N., Johnson, W. B., Lennard, C. J., & Turett, B.

citation count

  • 21

publication date

  • December 1997