Extensions of Yamamoto-Nayak's theorem (Q6541323)

A result of \textit{S. Nayak} [Linear Algebra Appl. 679, 231--245 (2023; Zbl 1529.15007)] asserts that \(\lim_{m\to \infty}|A^m|^{1/m}\) exists for each square complex matrix \(A\), where \(|A| = (A^*A)^{1/2}\). This extends the famous Beruling-Gelfand's spectral radius formula and its generalization by \textit{T. Yamamoto} [J. Math. Soc. Japan 19, 173--178 (1967; Zbl 0152.01404)]. The paper under review extends, with a different proof, the result of S. Nayak [loc. cit.] by proving \(\lim_{m\to \infty}|BA^mC|^{1/m}\) exists for any square complex matrices \(A, B\), and \(C\), where \(B\) and \(C\) are nonsingular. Extensions in the context of real semisimple Lie group are also given.