The induced norm of the schur multiplication operator with respect to the operator radius
Roy Mathias, K. Okubo · Linear and Multilinear Algebra · 1994
For any A∊Mn (the space of all nxn complex matrices) the Schur multiplication operator SA on Mn is defined by SA (X)=AoX(X∊Mn ) where o denotes the Schur product. We show that for 1≤p≤2, |SA |w ρ ≤ |SA |w where |SA |w ρ, |SA |w are the induced norms of SA with respect to the operator radius wρ (.) and the numerical radius w(.),respectively. In addition we show that for any p∊[1,2], and a variety of other results involving the induced norm of S A⊗B .