Convergence of ‘Periodic in the Limit’ Operator Continued Fractions
Robert C. Busby, Wyman G. Fair · SIAM Journal on Mathematical Analysis · 1979
By straightforward analysis, we prove a convergence theorem regarding continued fractions whose entries are members of a Banach algebra. If the entries converge fast enough to a certain fixed element, convergence is assured. Under suitable other restrictions, a stronger theorem results.