Vol. 45, No. 1, 1973

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Simultaneous approximation and interpolation in L1 and C(T)

Joseph Michael Lambert

Vol. 45 (1973), No. 1, 293–296

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).

Mathematical Subject Classification 2000
Primary: 41A65
Received: 21 November 1971
Revised: 17 April 1972
Published: 1 March 1973
Joseph Michael Lambert