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!

Luxottica owns many things, but the most important thing any company can own are distribution channels. Then you can just refuse to sell your competitor's goods.

That's how they took over Oakley. They cut off their distribution channels. Luxottica took over Sunglass Hut and pushed out Oakley. Oakley had to sell out to Luxottica. Then the prices for Oakley went way up.

Luxottica did something similar with Ray-Ban. Their products used to sell for around $19 in gas stations. After the Luxottica takeover, they became a "luxury" brand, with prices from $129 to $300.

They also manufacture almost all of the major glasses frame brands. They don't have a complete monopoly, but they do control a vast majority of the market.