On a Numerical Radius Preserving Onto Isometry on L(X). (12th October 2016) - Kim, Sun Kwang
Abstract : We study a numerical radius preserving onto isometry on L ( X ) . As a main result, when X is a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometry T on L ( X ) is numerical radius preserving if and only if there exists a scalar c T of modulus 1 such that c T T is numerical range preserving. The examples of such spaces are Hilbert space and L p spaces for 1 < p < ∞ .