On the numerical range behavior under the generalized Aluthge transform
David E. V. Rose, Ilya M. Spitkovsky · Linear and Multilinear Algebra · 2007
Let A = UR be the (right) polar decomposition of an n×n matrix A. The generalized Aluthge transform is then given by . We investigate the behavior of the numerical range W(Δλ(A)), and in particular its boundary, as a function of λ. We obtain complete results in the 2×2 case, when W(Δλ(A)) can be described explicitly, and then discuss which of the established properties persist in the general setting.