This is an announcement for the paper "Lipschitz extension constants equal projection constants" by Marc A. Rieffel.
Abstract: For a finite-dimensional Banach space $V$ we define its Lipschitz extension constant, $\cL\cE(V)$, to be the smallest constant $c$ such that for every compact metric space $(Z,\rho)$, every $X \subset Z$, and every $f: X \to V$, there is an extension, $g$, of $f$ to $Z$ such that $L(g) \le cL(f)$, where $L$ denotes the Lipschitz constant. Our main theorem is that $\cL\cE(V) = \cP\cC(V)$ where $\cP\cC(V)$ is the well-known projection constant of $V$. We obtain some consequences, especially when $V = M_n(\bC)$. We also discuss what happens if we also require that $|g|_{\infty} = |f|_{\infty}$.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 46B20; 26A16
Remarks: 12 pages. Intended for the proceedings of GPOTS05
The source file(s), liparc.tex: 35141 bytes, is(are) stored in gzipped form as 0508097.gz with size 12kb. The corresponding postcript file has gzipped size 61kb.
Submitted from: rieffel@math.berkeley.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0508097
or
http://arXiv.org/abs/math.FA/0508097
or by email in unzipped form by transmitting an empty message with subject line
uget 0508097
or in gzipped form by using subject line
get 0508097
to: math@arXiv.org.