On a Numerical Radius Preserving onto Isometry on L(X)

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 ct of modulus 1 such that ctt is numerical range preserving. the examples of such spaces are hilbert space and lp spaces for 1