Generalized roundness of the Schatten class,.

Abstract: In the paper Generalized roundness and negative type, Lennard, Tonge, and Weston show that the geometric notion of generalized roundness in a metric space is equivalent to that of negative type. Using this equivalent characterization, along with classical embedding theorems, the authors prove that for , fails to have generalized roundness q for any . It is noted, as a consequence, that the Schatten class , for , has maximal generalized roundness 0. In this paper, we prove that this result remains true for p in the interval . [Copyright &y& Elsevier]