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Journal of Function Spaces
Volume 2016 (2016), Article ID 9183135, 3 pages
http://dx.doi.org/10.1155/2016/9183135
Research Article

On a Numerical Radius Preserving Onto Isometry on

Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of Korea

Received 17 August 2016; Accepted 25 September 2016

Academic Editor: Ajda Fošner

Copyright © 2016 Sun Kwang Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a numerical radius preserving onto isometry on . As a main result, when is a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometry on is numerical radius preserving if and only if there exists a scalar of modulus 1 such that is numerical range preserving. The examples of such spaces are Hilbert space and spaces for .