Linear maps preserving ${\ell }_p$-norm parallel vectors

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

Two vectors $x,y$ in a normed vector space are parallel if there is a scalar $\mu$ with $|\mu |=1$ such that $\Vert x+\mu y\Vert =\Vert x\Vert +\Vert y\Vert$; they form a triangle equality attaining (TEA)…