Abstract measure algebras over homogeneous spaces of compact groups

Abstract

This paper presents a systematic study for abstract Banach measure algebras over homogeneous spaces of compact groups. Let [Formula: see text] be a closed subgroup of a compact group [Formula: see text] and [Formula: see text] be the left coset space associated to the subgroup [Formula: see text] in [Formula: see text]. Also, let [Formula: see text] be the Banach measure space consists of all complex measures over [Formula: see text]. Then we introduce the abstract notions of convolution and involution over the Banach measure space [Formula: see text].

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

“…The following paper extends our recent results concerning the abstract structure of involutions on some Banach algebras on homogeneous spaces [7,9,17] to more general settings. The mathematical theory of Banach convolution algebras plays significant and classical roles in abstract harmonic analysis, representation theory, functional analysis, operator theory, and C * -algebras, see [2,3,21,22,25,30,31,32,33,34] and references therein.…”

“…A unified operator theoretic approach introduced by Ghaani Farashahi, which gives a better understanding and characterization of the algebraic (convolution and involution) structure in both function and measure settings on the coset space G/H. In the case G is compact, analytic and algebraic aspects of this operator theoretic approach for functions studied at depth in [10,17] and in the settings of measures investigated extensively in [9]. Our results concerning operator theoretic characterization for structure of convolution and involution of functions defined on homogeneous spaces of compact groups [17], extended to the case G is locally compact and H is compact in [7].…”

Covariant Functions of Characters of Compact Subgroups

“…Then, for each x ∈ G and since λ H is a probability measure, we get [8,10]. Then, M 1 (G, H) consists of functions on G which are constant on cosets of N .…”

Orlicz Modules over Coset Spaces of Compact Subgroups in Locally compact Groups

“…For more details on harmonic analysis on homogeneous spaces of locally compact groups see [3,4,5,6,7,22,8].…”