\(\lambda\)-Aluthge iteration and spectral radius (Q930459)

The main result of this paper says that \(\lim_{n\to\infty} \|\Delta_\lambda^n(T)\|=r(T)\), where \(r(T)\) is the spectral radius of \(T\), holds true for an invertible operator \(T\in B(H)\) and a unitarily invariant norm \(\|\cdot\|\) under which \(B(H)\) is a Banach algebra with \(\| I \| =1\). Moreover, the author extends Yamazaki's formula for the spectral radius in terms of the \(\lambda\)-Aluthge transform \(\Delta_\lambda(T):=|T|^\lambda U|T|^{1-\lambda}\), where \(T = U |T|\) is the polar decomposition of \(T\).