Abstract. The notion of framings, recently emerging in [caz] as generalization of the reconstraction formula generated by pairs of dual frames, is in this note extended substantially. This calls on refining the basic dilation results which still being in the flavor of {\it théor?me principal} of B. Sz-Nagy [app] go much beyond it.

AMS Subject Classification (1991): 42C15, 47A20

Keyword(s): framings, dilations

Received January 17, 2013, and in revised form June 14, 2013. (Registered under 6/2013.)