Yamamoto's theorem for generalized singular values
Replacing the norm by some other geometric quantities in the spectral radius formula one can obtain the moduli of all eigenvalues of a given matrix. With the singular values this was done by \textit{T. Yamamoto} [J. Math. Soc. Japan 19, 173-178 (1967; Zbl 0152.014)], and with abstract s- numbers by \textit{H. König} [Studia Math. 65, 141-146 (1979; Zbl 0432.47010)], even for compact operators on Banach spaces. These results, however, are not deeper than the spectral radius formula; they are consequences of appropriate inequalities between the geometric quantities in question and the norms of suitable restrictions. In the paper under review, the authors prove such inequalities in the finite-dimensional case by exploiting the triangular form of the operator. The main results are, of course, particular cases of H. König's theorem (loc. cit.). A more general context is shown by the reviewer [Studia Math. 80, 219-234 (1984; Zbl 0542.47008)].
scientific article; zbMATH DE number 4152592