Abstract
<abstract><p>In this paper, we introduce and study the concept of hyper-instability as a strong version of multiplicative instability. This concept provides a powerful tool to study the multiplicative instability of Banach algebras. It replaces the condition of the iterated limits in the definition of multiplicative instability with conditions that are easier to examine. In particular, special conditions are suggested for Banach algebras that admit bounded approximate identities. Moreover, these conditions are preserved under isomorphisms. This enlarges the class of studied Banach algebras. We prove that many interesting Banach algebras are hyper-unstable, such as $ C^* $-algebras, Fourier algebras, and the algebra of compact operators on Banach spaces, each under certain conditions.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference15 articles.
1. J. L. Krivine, B. Maurey, Espaces de Banach stables, Isr. J. Math., 39 (1981), 273–295. https://doi.org/10.1007/BF02761674
2. N. Alabkary, A dynamical hierarchy of Banach algebras, Carleton University, 2022. https://doi.org/10.22215/etd/2022-15106
3. H. G. Dales, Banach algebras and automatic continuity, Oxford: Clarendon Press, 2000.
4. S. Ferri, M. Neufang, Multiplicative stability of Banach algebras, In Press.
5. M. Leinert, Remarks on Segal algebras, Manuscripta Math., 16 (1975), 1–9. https://doi.org/10.1007/BF01169059