Prince Alvaro did not have the title of Infante, but he did have the rank and honours.
Thanks. I also recently came across a reference to Prince Alvaro as Infante, and Infante Ferdinand de Baviera y Borbón as Duque de Cádiz. Things get so foggy when a family is long deposed. It is no wonder Juan Carlos felt the need to make a few clarifications after such a long interregnum.