On a Numerical Radius Preserving Onto Isometry on L(X). (12th October 2016)

• Record Type: Journal Article
• Authors: Kim, Sun Kwang
• Other Names: Fošner Ajda Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-10-12
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/9183135
• Languages: English
• ISSNs: 2314-8896

Abstract

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 < ∞ .