Abstract Structure of Measure Algebras on Coset Spaces of Compact Subgroups in Locally Compact Groups

2019/05/01 by Farashahi, Arash Ghaani
#43A15 #43A20 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Primary 43A85 #Secondary 43A10

paper · doi:10.48550/arxiv.1905.00226

Abstract

This paper presents a systematic operator theory approach for abstract structure of Banach measure algebras over coset spaces of compact subgroups. Let H be a compact subgroup of a locally compact group G and G/H be the left coset space associated to the subgroup H in G. Also, let M(G/H) be the Banach measure space consists of all complex measures over G/H. We then introduce an operator theoretic characterization for the abstract notion of involution over the Banach measure space M(G/H).

Related

• Measure Algebras on Homogeneous Spaces
• On Beurling measure algebras
• Banach Algebra of Complex Bounded Radon Measures on Homogeneous Space
• Convolution and involution on function spaces of homogeneous spaces
• Introverted subspaces of the duals of measure algebras