BSE-Properties of Second Dual of Banach Algebras

2022/01/16 by Ali Rejali, Rejali, Ali, Maryam Aghakoochaki +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2201.06105

openalex publication_date 2022/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a commutative semisimple Arens regular unital Banach algebra. The correlation between the BSE-property of the Banach algebra A and its second duals are assessed. It is found and approved that if A is a BSE-algebra, then so is A^**. The opposite correlation will hold in certain conditions. The correlation of the BSE-norm property of the Banach algebra and its second dual are assessed and examined. It is revealed that, if A is a commutative Arens regular unital Banach algebra where A^** is semisimple, then, A and A^** are BSE-norm algebra.

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