Cobos Díaz, FernandoKühn, Thomas2023-06-202023-06-2019890012-709410.1215/S0012-7094-89-05911-5https://hdl.handle.net/20.500.14352/57355Let H denote a Hilbert space, T a compact operator on H, {sn(T)}1 n=1 the eigenvalues of |T|, and Sp (p > 0) the set of all such T for which {sn(T)}1 n=1 is in `p. If A and B are bounded linear operators on L2, say that B pointwise dominates A if |A(x)(t)| B(|x|)(t) a.e. for all x(t) in L2. It is known that if p = 2n for some positive integer n, B is in Sp, and B pointwise dominates A, then A is also in Sp. Simon has conjectured that this result fails for p < 2, and has given a counterexample for 0 < p 1. The authors provide a counterexample for the remaining cases where 1 < p < 2.journal articlehttps//doi.org/10.1215/S0012-7094-89-05911-5http://projecteuclid.org/euclid.dmj/1077307842metadata only access517.98Trace idealsCompact operatorPointwise dominatesAnálisis funcional y teoría de operadores