Abstract: In this work we investigate n-widths of multiplier operators defined for functions on a complex sphere and bounded from L^p into L^q. We study lower and upper estimates for the n-widths of Kolmogorov, linear, of Gelfand and of Bernstein, of such operators. As application we obtain, in particular, estimates for the Kolmogorov n-width of classes of Sobolev, of finitely differentiable, infinitely differentiable and analytic functions on a complex sphere, in L^q, which are order sharp in various important situations Ver menos