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Generators and joint spectra for a special class of topological algebras | ||
| Journal of Mahani Mathematical Research | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 مرداد 1404 اصل مقاله (495.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24505.1732 | ||
| نویسندگان | ||
| Majid Sabet1؛ Ali Morovatpoor* 2 | ||
| 1Department of Mathematics, Faculty of Science, Payame Noor University (PNU), Tehran, Iran | ||
| 2Department of Basic Sciences, Faculty of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran | ||
| چکیده | ||
| Let $u$ be a generator for a commutative Banach algebra with unit. It is well known that the spectrum of $u$ is homeomorphic to the carrier of this algebra. In this paper, we extend this result for a broader class of complete metrizable topological algebras, particularly those satisfying the properties of fundamental strongly sequential(FSS) and linearly complete algebras. Specifically, we establish that the homeomorphism between the spectrum Sp(u) and the carrier space holds for FSS-algebras and linearly complete regular algebras. Thus, we generalize the classical result known for Banach algebras. Furthermore, by assuming that the boundedness radius $\beta$ is subadditive, we prove that the spectrum $Sp(u)$ is polynomially convex. This assumption also enables us to derive a more general result on the polynomial convexity of joint spectra in finitely generated algebras. To demonstrate the significance and nontrivial nature of these extensions, we provide illustrative examples that highlight how the introduced conditions substantially broaden the applicability of existing results. | ||
| کلیدواژه‌ها | ||
| Strongly sequential algebras؛ Fundamental algebras؛ Boundedness radius؛ Carrier space؛ Joint generators | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 7 تعداد دریافت فایل اصل مقاله: 7 |
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