A Note on the Convergence of Certain Non-Commutative Continued Fractions

摘要

It is assumed that the coefficients of a non-commutative continued fraction are members of a normed ring; the supremum norm of A is denoted by Gamma(A), the infinimum norm by lambda(A). If gamma(c sub 2) + gamma(c sub 3) + summation, s=4 to s=r, of the following: gamma(c sub 5)(1 + gamma(c sub 2)) (1 + gamma(c sub 3))...(1 + gamma(c sub(s-2)))