Generalized roundness of the Schatten class,

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 , L p fails to have generalized roundness q for any q > 0 . It is noted, as a consequence, that the Schatten class C p , 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 ) .