Maps preserving numerical radius distance on ${\rm C}^*$-algebras
Volume 162 / 2004
Studia Mathematica 162 (2004), 97-104
MSC: Primary 47B49, 47A12; Secondary 47H20.
DOI: 10.4064/sm162-2-1
Abstract
We characterize surjective nonlinear maps ${\mit \Phi } $ between unital C*-algebras ${\mathcal A}$ and ${\mathcal B}$ that satisfy $w({\mit \Phi } (A)-{\mit \Phi } (B))=w(A-B)$ for all $A,B\in {\mathcal A}$ under a mild condition that ${\mit \Phi } (I)-{\mit \Phi } (0)$ belongs to the center of ${\mathcal B}$, where $w(A)$ is the numerical radius of $A$ and $I$ is the unit of ${\mathcal A}$.
