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

abstract

  • A renorming of ℓ, 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 ℓ inside any isomorphic copy of ℓ 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.

author list (cited authors)

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

citation count

  • 17

complete list of authors

  • Dowling, PN||Johnson, WB||Lennard, CJ||Turett, B

publication date

  • January 1997