Abstract
A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product S 2 ×S 2 of two copies of the Hilbert-Schmidt classes into the trace class S 1 is established in terms of linear Schur multipliers acting on the space S 1 of all compact operators. Using this formula, we resolve Peller's problem on Koplienko-Neidhardt trace formulae. Namely, we prove that there exist a twice continuously differentiable function f with a bounded second derivative, a self-adjoint (unbounded) operator A and a self-adjoint operator B 2 S 2 such that f(A + B) f(A) d dt (f(A + tB)) � t=0 / 2 S 1 .
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