The optimality of James’s distortion theorems
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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.
complete list of authors
Dowling, PN||Johnson, WB||Lennard, CJ||Turett, B