Nicolas Jp

Low-Dimensional Thresholds and Optimal Weighted-Shift Bounds for the Aluthge Transform

Let \(A=U|A|\) be a complex matrix and let \(\Delta_\lambda(A)=|A|^\lambda U|A|^{1-\lambda}\), \(0<\lambda<1\), be its \(\lambda\)-Aluthge transform. Huang and Tam conjectured that the Frobenius norm of the self-commutator is contractive under \(\Delta_\lambda\). Following Zhang'...

The complete singular-value spectrum of a twisted commutator with a rank-one factor and an application to the weighted Böttcher–Wenzel inequality

Let \(D\) be positive definite Hermitian and let \(T_X:Y\mapsto XDY-YDX\) be the associated twisted commutator on \(M_n(\mathbb C)\) with the Frobenius norm. For a rank-one factor \(X=\sigma uv^*\), an orthogonal block decomposition gives the exact operator norm \[\lVert T_X\rVer...