Caffè Pedrocchi commands great historic importance for this town. It was founded 180 years ago and witnessed a critical involvement in Italian revolutions and intellectual activity. (I will discuss this in a later post.)
The no-doors refers to the fact that it is always open to the public. In fact, there is a room, The Green Room, where you can sit quietly and read or do whatever you want that is silent without having to order anything from the bar. It's a great, quiet and elegant refuge between appointments for me sometimes when it's raining and I just want to read a magazine.
The important news now is that the café is expanding. The Museo del Risorgimento is going to move to Palazzo Zuchermann and open up all the upper levels of the historic building. The café plans to expand its seating area upstairs, maybe stay open later in the evening (after 8 p.m.) and build luxury rental spaces as a foresteria for artists, intellectuals, etc.
The city is debating whether they should raise the café's rent after the expansion (and natural increase in revenue). Currently it pays a subsidized Euro 500 ($715)/month while it charges nearly Euro 3 ($5) for a coffee! That rent is what I paid for an ugly 35-square-meter (380 square foot) apartment.
Caffè Pedrocchi link.
Il Mattino article about the subject.