Ideal F-Norms on C*-Algebras. II

Abstract

© 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 seminorm ‖·‖p for 1 ≤ p< +∞. Weestimate the distance from any element of a unital A to the scalar subalgebra in the seminorm ‖·‖1. We investigate geometric properties of semiorthogonal projections from A. If a trace φ is finite, then the set of all finite sums of pairwise products of projections and semiorthogonal projections (in any order) of A with coefficients from ℝ+ is not dense in A.