Linear maps of $C^{\ast }$-algebras preserving norm parallelism

Chi-Kwong Li, Ming-Cheng Tsai, Ya-Shu Wang +1

Two elements $a,b$ in a normed space are parallel if $\Vert a+\gamma b\Vert =\Vert a\Vert +\Vert b\Vert$ for some $|\gamma |=1$; they form a triangle equality attaining (TEA) pair if $\Vert a+b\Vert =\Vert a\Vert +\Vert b\Vert$. For finit…