On the Banach–Steinhaus Theorem for Hemi-Banach Algebras

Liaqat Ali, Muhammad Aslam, Muna Alhodieb, Jongsuk Ro and Eman Ghareeb Rezk

Journal of Mathematics, 2026, vol. 2026, 1-9

Abstract: Hemi-normed algebras may be considered as a natural extension of normed algebras. The aim of this paper is to introduce notions of hemi-normed algebras and hemi-Banach algebras and to develop their foundational theory. In this framework, we establish the fundamental results on the spectrum and prove the Banach–Steinhaus theorem in hemi-Banach algebras. As a consequence, we target the conclusion that every derivation on a unital hemi-Banach algebra is continuous.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8967980

DOI: 10.1155/jom/8967980

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