On the Ptolemy constant of Lorentz sequence spaces and their duals

Abstract

The Ptolemy constant of two-dimensional Lorentz sequence spaces is computed in this paper. On the way, we also calculate the Ptolemy constant in the dual space of two-dimensional Lorentz sequence spaces in the case of q = 1 and q 2. Moreover, we determine the Ptolemy constant of absolute normalized norms under some new conditions. These results which not only contain some previous results, but also give the exact value of the Ptolemy constant in some concrete Banach spaces.