On generalized numerical range of the Aluthge transformation.
Let \(T\) be a bounded linear operator on a Hilbert space. The Aluthge transform \(\widetilde{T}\) of \(T\) is given by \(\widetilde{T} =| T| ^{1/2}U| T| ^{1/2}\) where \(T=U | T | \) is the polar decomposition of \(T\). The authors show that the Aluthge transformation \(\widetilde T\) of a matrix \(T\) and a polynomial \(f\) satisfy the inclusion \(W_C(f(\widetilde T))\subset W_C(f(T))\) for the generalized numerical range \(W_C(\cdot)\) if \(C\) is a Hermitian matrix or a rank-one matrix.
scientific article; zbMATH DE number 1970615
scientific article