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In this paper various inequalities between the operator norm and its numerical radius are provided. For this purpose, we employ some classical inequalities for vectors in inner product spaces due to Buzano, Goldstein-Ryff-Clarke, Dragomir-S ´andor and the author.doi:10.5556/j.tkjm.39.2008.40 fatcat:dsevubxo45co3ghmrgobfeyyoi