HTML and CSS provide no means to trigger full screen mode for an element. JavaScript is your only option.
HTML 5 introduces a full screen API for JavaScript. It is still experimental, so you need to use prefixed property names in some browsers and it won't work at all in others.
function makeFullScreen(element) {
    if (element.requestFullScreen) {
        element.requestFullScreen();
    } else if (element.webkitRequestFullScreen) {
        element.webkitRequestFullScreen();
    } else if (element.mozRequestFullScreen) {
        element.mozRequestFullScreen();
    } else if (element.msRequestFullScreen) {
        element.msRequestFullScreen();
    } 
}
You then just need to bind an event handler to call it.
document.addEventListener('keypress', function (evt) {
  if (evt.altKey && evt.keyCode === 32) {
     makeFullScreen(document.querySelector('div')); 
  }
});
Beware of depending on modifier keys though. On my system, alt + space is captured at the OS level (to open Spotlight) so it will never reach the browser.