General resolution of a convergence question of L. Krukier

It was shown that there exists a matrix norm N such that N ( A −1 B )<1 if A, B ∈ M n (), 0∉ F ( A ), and g ( A, B )<1 where g ( A, B )=max| z |, z ∈ G ( A, B ),\documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}\begin{eqnarray*}G(A,B) = \left\{\frac{x^{*}Bx}{x^{*}Ax}:x \in {\mathscr{C}}^{n},x^{*}x = 1\right\}\end{eqnarray*}\end{document}Copyright © 2009 John Wiley & Sons, Ltd.