  In previous papers, we used abstract potential theory, as developed by
Fuglede and Ohtsuka, to a systematic treatment of rendezvous numbers. We
introduced energies, Chebyshev constants as two variable set functions, and the
modified notion of rendezvous intervals which proved to be rather nicely
behaved even for only lower semicontinuous kernels or for not necessarily
compact metric spaces.
  Here we study the rendezvous and average numbers of possibly infinite
dimensional normed spaces. It turns out that very general existence and
uniqueness results hold for the modified rendezvous numbers in all Banach
spaces. We also observe the connections of these "magical numbers" to Chebyshev
constants, Chebyshev radius and entropy. Applying the developed notions with
the available methods we calculate the rendezvous numbers or rendezvous
intervals of certain concrete Banach spaces. In particular, a satisfactory
description of the case of L_p spaces is obtained for all p>0.
