I'm not sure about the monopoly accusation, but Luxottica's influence extends far beyond the US, and is not just retail. The company owns over 7000 retail outlets across North and South America, Asia-Pacific, China, South Africa and the Middle East, under well-known retail brands such as Sunglass Hut, LensCrafters, OPSM and others.

Moreover, Luxottica are vertically-integrated, controlling design, manufacture and distribution of many major brands in both prescription and fashion eyewear. Their in-house brands include Arnette, Oakley, Oliver Peoples, Persol, Ray-Ban, Vogue and others. Additionally they manufacture product under license for many more, like Brooks Brothers, Chanel, D&G, DKNY, Ralph Lauren, Prada, Tiffany and Versace.

So, monopoly or not, it's fair to say that Luxottica exerts considerable control over the worldwide eyewear market!