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 p>2, Lp fails to have generalized roundness q for any q>0. It is noted, as a consequence, that the Schatten class Cp, for p>2, has maximal generalized roundness 0. In this paper, we prove that this result remains true for p in the interval (0,2).
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