One-parameter groups of orthogonality preservers on JB${}^{\ast }$-algebras

Abstract

In a first objective we improve our understanding about surjective and bijective bounded linear operators preserving orthogonality from a JB${}^{\ast }$-algebra $\mathcal{A}$ into a JB${}^{\ast }$-triple $E$. Among many other conclusions, it is shown that a bounded linear bijection $T:\mathcal{A}\to E$ is orthogonality preserving if, and only if, it is biorthogonality preserving if, and only if, it preserves zero-triple-products in both directions (i.e., $\{a,b,c\}=0\iff \{T(a),T(b),T(c)\}=0$). In the second main result we establish a complete characterization of all one-parameter groups of orthogonality preserving operators on a JB${}^{\ast }$-algebra.

arXiv admin note: substantial text overlap with arXiv:2004.04155