RT Journal Article
T1 On a Conjecture of Barry Simon on Trace Ideals
A1 Cobos Díaz, Fernando
A1 Kühn, Thomas
AB Let 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.
PB DUKE UNIV PRESS
SN 0012-7094
YR 1989
FD 1989
LK https://hdl.handle.net/20.500.14352/57355
UL https://hdl.handle.net/20.500.14352/57355
DS Docta Complutense
RD 7 abr 2025