Luke has been a very kind and considerate host as well as his friend who came to clean and check me in as soon as I arrived (they are living right next to the apartment). Luke always answered to my messages right away. As my flight had been very early I needed to take a rest once I arrived and Luke made it possible for me to check in even earlier than noon. Thank you Luke!!
Apart from the apartment not being located right in the centre of Milan, it's a great place to stay, you can get to the Duomo (right in the centre) directly by taking the tram (no.3) which stops in front of the building. The view from the apartment on the 13th floor is super nice, it's a quiet neighborhood (which means I slept very well in the double bed) and there is a supermarket close by as well as it was possible to order a pizza by phone.