Parallelism in Hilbert $K(\mathcal{H})$-modules

Abstract

Let $\mathcal{H}$ be a Hilbert space and $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert $K(\mathcal{H})$-module $\mathcal{E}$ by employing the minimal projections on $\mathcal{H}$. In addition, we give some equivalence assertions about the norm-parallelism of compact operators on a Hilbert $C^*$-module.