On the joint numerical radius parallelism of operators. (English) Zbl 1529.47010
Summary: Let \(\mathcal{B}(\mathcal{H})\) denote the set of all bounded linear operators acting on a complex Hilbert space \(\mathcal{H}\), and let \(n\geq 1\). In this paper, we define the concept of almost joint numerical radius parallelism on \(\mathcal{B}(\mathcal{H})^n\). Necessary and sufficient conditions for \(n\)-tuples of operators \(\mathbf{A}\) and \(\mathbf{B}\) in \(\mathcal{B}(\mathcal{H})^n\) to be almost parallel are obtained. Other results are also derived.
MSC:
| 47A13 | Several-variable operator theory (spectral, Fredholm, etc.) |
| 47A12 | Numerical range, numerical radius |
| 47B49 | Transformers, preservers (linear operators on spaces of linear operators) |
| 46B20 | Geometry and structure of normed linear spaces |
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