In this paper we study the notion of sectorial operator in a Hilbert space . According to the stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600" and this is equivalent to a certain inverse estimate valid outside . In this thesis we see that the validity of the same estimate but with a factor bigger than one , is equivalent to the validity of a certai strengthened Cauchy-Schwarz inequality for all pairs w , Aw. This extends the original characterization in terms of numerical range by a more general characterization based on a normalized numerical range . We also observe numerical range can be computed numerically.