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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<p<∞

journal of function spaces

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On a Numerical Radius Preserving Onto Isometry onL(X)