A NOTE ON THE CONVERGENCE OF CERTAIN NON-COMMUTATIVE CONTINUED FRACTIONS.
Abstract
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)))<1 then the convergents of both continued fractions pre(c sub 0 + (c sub 1/1+)(c sub 2/1+)...) and post(c sub 0 + (c sub 1/1+)(c sub 2/1+)...) exist, and both continued fractions converge uniformly. A further convergence result is derived.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1967
- Accession Number
- AD0657577
Entities
People
- P. Wynn
Organizations
- University of Wisconsin–Madison