We study maps of positive operators of the Schatten -classes (), which preserve the -norms of convex combinations, that is, . They are exactly those carrying the form for a unitary or antiunitary . In the case , we have the same conclusion whenever it just holds for all the positive Hilbert-Schmidt class operators of norm . Some examples are demonstrated.
David Li-Wei Kuo. Ming-Cheng Tsai. Ngai-Ching Wong. Jun Zhang. "Maps Preserving Schatten -Norms of Convex Combinations." Abstr. Appl. Anal. 2014 (SI52) 1 - 5, 2014. https://doi.org/10.1155/2014/520795