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

M. Mohammadi Gohari, M. Amyari

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.

Tbilisi Mathematical Journal, Vol. 12(2) (2019), pp. 67-75