DOI: 10.1155/jom/8967980 ISSN: 2314-4629

On the Banach–Steinhaus Theorem for Hemi‐Banach Algebras

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

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