The main windows of the new ILORI store on a corner in New York’s fashionable SoHo district give little away. On a thick sheet of translucent glass, a projector throws up images of fire and volcanoes behind a representation of a flaming phoenix.

The store is owned by Luxottica, the Italian eyewear company, which is hoping to persuade more Americans that sunglasses, like handbags or watches, are an essential luxury accessory.