Abstract
In this paper, we study the numerical radius parallelism for bounded linear operators on a Hilbert space \(\big ({\mathscr {H}}, \langle \cdot ,\cdot \rangle \big )\). More precisely, we consider bounded linear operators T and S which satisfy \(\omega (T + \lambda S) = \omega (T)+\omega (S)\) for some complex unit \(\lambda \), and is denoted by \(T \parallel _{\omega } S\). We show that \(T \parallel _{\omega } S\) if and only if there exists a sequence of unit vectors \(\{x_n\}\) in \({\mathscr {H}}\) such that
We then apply it to give some applications.
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Communicated by Hamid Reza Ebrahimi Vishki.
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Mehrazin, M., Amyari, M. & Zamani, A. Numerical Radius Parallelism of Hilbert Space Operators. Bull. Iran. Math. Soc. 46, 821–829 (2020). https://doi.org/10.1007/s41980-019-00295-3
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DOI: https://doi.org/10.1007/s41980-019-00295-3