On a Numerical Radius Preserving Onto Isometry onL(X)

Abstract

We study a numerical radius preserving onto isometry onL(X). As a main result, whenXis a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometryTonL(X)is numerical radius preserving if and only if there exists a scalarcTof modulus 1 such thatcTTis numerical range preserving. The examples of such spaces are Hilbert space andLpspaces for1<p<∞.