L₁- Properties of vector-valued Banach algebras

2022/12/18 by Maryam Aghakoochaki, Aghakoochaki, Maryam, Ali Rejali +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2212.09106

Abstract

Let G be a locally compact group and A be a commutative semisimple Banach algebra over the scalar field ℂ. The correlation between different types of BSE- Banach algebras A, and the Banach algebras L¹(G, A) are assessed. It is found and approved that M(G, A) = L¹(G, A) if and only if G is discrete. Furthermore, some properties of vector-valued measure algebras on groups are given, so that M(G, A) is a convolution measure algebra.

Related

• C^*- properties of vector-valued Banach algebras
• BSE-properties of Vector-valued group algebras
• The BSE-property for vector-valued L^p-algebras
• C^∗-algebra structure on vector valued-Banach algebras
• Measure Algebras on Homogeneous Spaces