From: Dave Rusin <rusin@math.niu.edu>
Date: Wed, 18 Nov 1998 15:37:59 -0600 (CST)
To: bruck@math.usc.edu
Subject: Re: optimal shape
Newsgroups: sci.math

>I like the norm in L^4; I would have loved it
>to have some bizarre property like this.  L^4 DOES have the property that
>if S is any subset of it, and T : S --> L^4 is an isometry which can be
>extended to a nonexpansive mapping T' : clco S --> L^4 (nonexpansive =
>has Lipschitz constant one), then T' must be an isometry.  That's false 
>in L^6 and L^3.  (It IS true in L^2, of course.  In fact, isometries can
>be extended to isometries in Hilbert space.)

Can you elaborate? What's the property of  4  necessary here?
dave