The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra
UDC 517.5 We establish the relationship between the S-spectrum of $fg$ and the S-spectrum of $\alpha f+\beta g,$ where $f$ and $g$ are two idempotents on a two-sided quaternionic Banach algebra $\mathcal{A}$ and $\alpha, \beta\in\mathbb{R}.$ We also study the invertibility of linear combinations of...
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8410 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
We establish the relationship between the S-spectrum of $fg$ and the S-spectrum of $\alpha f+\beta g,$ where $f$ and $g$ are two idempotents on a two-sided quaternionic Banach algebra $\mathcal{A}$ and $\alpha, \beta\in\mathbb{R}.$ We also study the invertibility of linear combinations of idempotents on $\mathcal{A}.$ To do this, we define the complexification $\mathcal{A}_c$ of $\mathcal{A},$ which is regarded as a real Banach algebra, and establish the relationship between the S-spectrum of $a \in \mathcal{A}$ and the spectrum of $a$ as an element of the complexification $\mathcal{A}_c.$ |
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| DOI: | 10.3842/umzh.v77i11.8410 |