2018/12/01 by M. Mohammadi Gohari, Gohari, M. Mohammadi, Maryam Amyari +1
Mathematics · Computer Science · #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1812.00167
Let H be a Hilbert space, and let K(H) be the C^*-algebra of compact operators on H. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert K(H)-module by employing the Birkhoff--James orthogonality. Among other things, we present a characterization of transitive relation of the norm-parallelism for elements in a certain Hilbert K(H)-module. We also give some characterizations of the Schatten p-norms and the operator norm-parallelism for matrices.