ThispapershowsthatXisuniformlynon-squareiffP(η_o)>0forsomeη_o∈(0,2).ThusXissuper-reflexiveifandonlyifforXthereexistsanequivalentnormwhichmeetstheabovecondition.Byvirtueofthebeforementionedresult,theauthorderivesthenecessary,andsuffi-cientconditionsforXandl~p(X_j)beinguniformlynon-square,respectively,andgivesacharacterizationoffinite-dimensionalspaceswhichareuniformlynon-square.
