On the numerical radius parallelism and the numerical radius Birkhoff orthogonality
Functional Analysis
2024-12-03 v1
Abstract
In this paper, we generalize the notions of numerical radius parallelism and numerical radius Birkhoff orthogonality, originally formulated for operators on Hilbert spaces, to operators on normed spaces. We then proceed to demonstrate their fundamental properties. Notably, our findings reveal that numerical radius parallelism lacks transitivity, and numerical radius Birkhoff orthogonality is neither left nor right additive. Additionally, we offer characterizations for both concepts. Furthermore, we establish a connection between numerical radius parallelism and numerical radius Birkhoff orthogonality.
Keywords
Cite
@article{arxiv.2412.01735,
title = {On the numerical radius parallelism and the numerical radius Birkhoff orthogonality},
author = {Jiaye Bi and Huayou Xie and Yongjin Li},
journal= {arXiv preprint arXiv:2412.01735},
year = {2024}
}