The operator--valued parallelism and norm-parallelism in matrices
Functional Analysis
2018-12-04 v1
Abstract
Let be a Hilbert space, and let be the -algebra of compact operators on . In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert -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 -module. We also give some characterizations of the Schatten -norms and the operator norm-parallelism for matrices.
Cite
@article{arxiv.1812.00167,
title = {The operator--valued parallelism and norm-parallelism in matrices},
author = {M. Mohammadi Gohari and M. Amyari},
journal= {arXiv preprint arXiv:1812.00167},
year = {2018}
}