Some Results on Absolute Projection Constants. (2nd January 2019) - Castejón, Alberto; Lewicki, Grzegorz; Martín, Alberto
Abstract: Let V be an n -dimensional real or complex Banach space and letλ ( V ) denote its absolute projection constant. For anyN ∈ N, N ≥ n defineλ n N = sup { λ ( V ) : d i m ( V ) = n, V ⊂ l ∞ ( N ) } . In this article, we determine, in the complex case, minimal projections with respect to l 1 -norm as well as with respect tol ∞ -norm for subspaces given by solutions of certain extremal problems. As an application we show that for anyn, N ∈ N, N ≥ n, there exists an n -dimensional subspaceV n ⊂ l 1 ( N ) such thatλ n N = λ ( V n, l 1 ( N ) ) . This generalizes the results from Castejon and Lewicki (2014) obtained in the real case.