Abstract:We classify $n\times n$-matrix-valued continuous commutativity and spectrum preservers defined on spaces of (a) normal, (b) semisimple and (c) arbitrary $n\times n$ matrices with spectra contained in sufficiently connected subsets $\mathcal{X}\subseteq \mathbb{C}$, generalizing a number of results due to Šemrl, Gogić, Tomašević and the author among others. In case (a) these are always conjugations or transpose conjugations, while in cases (b) and (c) qualitatively distinct possibilities arise depending on the local regularity of the complex-conjugation map close to coincident-eigenvalue loci of $\mathcal{X}^n$.
From: Alexandru Chirvăsitu L. [view email]
[v1]
Wed, 8 Apr 2026 13:11:43 UTC (13 KB)
[v2]
Mon, 29 Jun 2026 13:42:12 UTC (13 KB)
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