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- W4300005528 abstract "A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product $mathcal S^2times mathcal S^2$ of two copies of the Hilbert-Schmidt classes into the trace class $mathcal S^1$ is established in terms of linear Schur multipliers acting on the space $mathcal S^infty$ 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 $Bin mathcal S^2$ such that $$ f(A+B)-f(A)-frac{d}{dt}(f(A+tB))bigvert_{t=0}notin mathcal S^1. $$" @default.
- W4300005528 created "2022-10-03" @default.
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- W4300005528 date "2015-04-15" @default.
- W4300005528 modified "2023-09-27" @default.
- W4300005528 title "Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae" @default.
- W4300005528 doi "https://doi.org/10.48550/arxiv.1504.03843" @default.
- W4300005528 hasPublicationYear "2015" @default.
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