heeelllooo dpm and welcome

thats a long span without a central supporting bracket or leg
when you say solid i assume you mean laminated from several widths as you cant generaly get 12" boards apart from the fact one that wide being unstable
light loading on that span is a few nick nacks and some books

if you dont want to have a central support you can front it with a bit of 2x1 with a rebate of 10x20mm for the shelve to glue into
or if you use 3x1 you could fit a cupboard strip lamp underneath in this form i would be happy to load with books as long as the 3 closed sides are on a batton
if you dont want to front with additonal timber make shure you firmly screw at the back corners as this will give additional support to the front edge
http://www.screwfix.com/app/sfd/cat/pro.jsp?id=80146&ts=36784