Given a dense subspace of
M of a Banach space X, an element x in X and a finite collection of linear functions
in X∗, the problem of simultaneous approximation and interpolation is to interpolate
x at the given functionals in X∗ by an element m of M, with the restriction that the
norms of x and m be equal and their difference in norm be arbitrarily small. A
solution is given for the space L1 with dense subspace, the simple functions in L1,
and any collection of functions in L∞. In addition the problem is studied in the space
C(T), with any dense subalgebra and any finite collection of linear functionals in
C(T)∗.
