Setup different languages for WordPress admin and front end

wordpress.different-langauges.php

     // setup one language for admin and the other for theme
     // must be called before load_theme_textdomain()

     function set_my_locale($locale) {
          $locale = ( is_admin() ) ? "en_US" : "it_IT";
          setlocale(LC_ALL, $local );
          return $locale;
     }
     add_filter( 'locale', 'set_my_locale' );