The optimality of James's distortion theorems
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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.