The Arens-Calderon theorem forcommutative topological algebras

• M. Weigt ^[2] ; Ioannis Zarakas ^[1]
  1. [1] National and Kapodistrian University of Athens

     National and Kapodistrian University of Athens

     Dimos Athens, Grecia

     
  2. [2] Department of Mathematics, Summerstrand Campus (South) Nelson Mandela University, 6031 Port Elizabeth (Gqeberha), South Africa
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 39, Nº 1, 2024, págs. 19-35
• Idioma: inglés
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• Resumen

  • A theorem of Arens and Calderon states that if A is a commutative Banach algebra with Jacobson radical Rad(A), and if a0 , . . . , an∈ A with a0 ∈ Rad(A) and a1 an invertible element of k A, then there exists y ∈ Rad(A) such that Σ ak yk = 0. In this paper, we give extensions of this result to commutative non-normed topological algebras, as this is vital for extending an embedding theorem of Allan in [2] regarding the embedding of the formal power series algebra C[[X]] into a commutative Banach algebra