Best approximation in Chebyshev subspaces of L(l1n,l1n)

Abstract

Abstract. Chebyshev subspaces of L(l n 1 , l n 1 ) are studied. A construction of a k-dimensional Chebyshev (not interpolating) subspace is given.

The unicity of best approximation in a space of compact operators

“…This result is quite different from the result obtained in [7]. In the space L (l n 1 , c 0 ) any finite-dimensional Chebyshev subspace is an interpolating subspace.…”

Operator Algebras and Mathematical Physics

“…Since the matrix T (g, L), with matrix elements M (g, L) rk , constitutes a representation of GL(2, C) on the subspace H L (C) of H(C), generated by the basis S(L), we know that T (g, L) −1 = T (g −1 , L). From (53) it also follows that T (g, L) * = T (g * , L). Thus the second equality in (60) follows.…”