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

الملخص EN

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