We introduce it compressed training adaptive equalization as a novel approach for reducing number of training symbols in a communication packet. The proposed semi-blind approach is based on the exploitation of the special magnitude boundedness of communication symbols. The algorithms are derived from a special convex optimization setting based on l_\infty norm. The corresponding framework has a direct link with the compressive sensing literature established by invoking the duality between l_1 and l_\infty norms. Through this link, it is possible to adapt various research results in sparse signal processing literature to adaptive equalization problem. In fact, through utilization of such a link, we show that the amount of training data needed is in the order of the logarithm of the channel spread (or equalizer length) in the fractionally spaced equalization scenario. The numerical experiments provided validates the analytical results and the potentials of the proposed approach.