For a Banach space V we define its Lipschitz extension constant, (V), to be the infimum of the constants c such that for every metric space (Z,ρ), every X⊂Z, and every f:X→V
Nearby in the stack
, there is an extension,
g
, of
f
to
Z
such that
L(g)≤cL(f)
, where
L
denotes the Lipschitz constant. The basic theorem is that when
V
is finite-dimensional we have
(V) = (V)
where
(V)
is the well-known projection constant of
V
. We obtain some direct consequences of this theorem, especially when
V = M_n()
. We then apply techniques for calculating projection constants, involving averaging projections, to calculate
((M_n())^sa)
. We also discuss what happens if we also require that