$\rm BSE$ norm for Abstract Segal algebras
Abstrak
Let $(\mathcal A,\|\cdot\|_{\mathcal A})$ be a commutative and semisimple Banach algebra and $(\mathcal B,\|\cdot\|_{\mathcal B})$ be an abstract Segal algebra with respect to $\mathcal A$. In this paper, we first recall and study three important and practical mappings ${}_{\mathcal A}L$, $\Gamma_1$ and $\Gamma_2$. Then we investigatewhenever these mappings have closed ranges. In fact, we research and study the conditions, under which having closed range of one of these mappings implies having the closed range of the another mapping. After that, using these results, we give a necessary and sufficient condition for $(\mathcal B,\|\cdot\|_{\mathcal B})$, to be an algebra with $\rm BSE$ norm. Finally, we generalize some general results about abstract Segal algebras with respect to natural Banach functional algebras for abstract Segal algebras with respect to arbitrary Banach algebras. Also, throughout the paper, we provide examples to clarify the stated content.
Topik & Kata Kunci
Penulis (2)
Fatemeh Abtahi
Maryam Toutounchi
Akses Cepat
- Tahun Terbit
- 2025
- Sumber Database
- DOAJ
- DOI
- 10.22108/msci.2024.141063.1653
- Akses
- Open Access ✓