Minimal projections onto hyperplanes in vector-valued sequence spaces

In this paper we present a lower bound for the relative projection constant λ(V,X)λ(V,X), where VV is a hyperplane in XX and XX is a vector-valued sequence space c0({Xn}n∈N)c0({Xn}n∈N) or l1({Xn}n∈N)l1({Xn}n∈N). We give a characterization of one-complemented hyperplanes in c0({Xn}n∈N)c0({Xn}n∈N). We also consider projections of norm one in l1({Xn}n∈N)l1({Xn}n∈N). Moreover some applications of obtained results will be presented.