A NOTE ON THE CONVERGENCE OF CERTAIN NON-COMMUTATIVE CONTINUED FRACTIONS.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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 GammaA, the infinimum norm by lambdaA. If gammac sub 2 gammac sub 3 summation, s4 to sr, of the following gammac sub 51 gammac sub 2 1 gammac sub 3...1 gammac subs-21 then the convergents of both continued fractions prec sub 0 c sub 11c sub 21... and postc sub 0 c sub 11c sub 21... exist, and both continued fractions converge uniformly. A further convergence result is derived.
- Theoretical Mathematics