© 2019, Allerton Press, Inc. We study ideal F-norms ‖·‖p, 0 <p < +∞ associated with a trace ϕ on a C*-algebra A. If A, B of A are such that |A|≤ |B|,then ‖A‖p ≤ ‖B‖p. We have ‖A‖p = ‖A*‖p for all A from A (0 <p < +∞)and a ...