In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space H with singular values the same order as the harmonic sequence.
Weak trace-class operators feature in the noncommutative geometry of French mathematician Alain Connes.
A compact operator A on an infinite dimensional separable Hilbert space H is weak trace class if μ(n,A) = O(n−1), where μ(A) is the sequence of singular values.
In mathematical notation the two-sided ideal of all weak trace-class operators is denoted, where
[clarification needed] The term weak trace-class, or weak-L1, is used because the operator ideal corresponds, in J. W. Calkin's correspondence between two-sided ideals of bounded linear operators and rearrangement invariant sequence spaces, to the weak-l1 sequence space.