The Operator-Valued Parallelism and Norm-Parallelism in Matrices

M. Mohammadi Gohari () and M. Amyari ()
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M. Mohammadi Gohari: Islamic Azad University
M. Amyari: Islamic Azad University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1305-1316

Abstract: Abstract 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.

Keywords: Hilbert C*-module; orthonormal basis; parallelism; Schatten p-norm; 46L08; 47A30; 47B10; 47B47 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0467-8

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