2015/04/15 by Clément Coine, Christian Le Merdy, Coine, Clément +7 · 2 citations
Mathematics · #47A55 #47A56 #47B10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A55 #msc:47A56 #msc:47B10
paper · pdf · doi:10.48550/arxiv.1504.03843
arxiv created 2015/04/15 · arxiv updated 2015/04/16
A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product \mathcal S2× \mathcal S2 of two copies of the Hilbert-Schmidt classes into the trace class \mathcal S1 is established in terms of linear Schur multipliers acting on the space \mathcal S^∞ 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∈ \mathcal S2 such that f(A+B)-f(A)-(d)/(dt)(f(A+tB))\vertt=0∉ \mathcal S1.