  In a recent work, we analyzed a weighted-residual error estimator for
isogeometric boundary element methods in 2D and proposed an adaptive algorithm
which steers the local mesh-refinement of the underlying partition as well as
the multiplicity of the knots. In the present work, we give a mathematical
proof that this algorithm leads to convergence even with optimal algebraic
rates. Technical contributions include a novel mesh-size function which also
monitors the knot multiplicity as well as inverse estimates for NURBS in
fractional-order Sobolev norms.
