Continuous field of Orlicz space on locally compact groupoids and related results

2025/01/10 by Karthik Sridharan, K. N. Sridharan, Sridharan, K. N. +2
Decision Sciences · Computer Science · Mathematics · #Fuzzy and Soft Set Theory #Advanced Algebra and Logic #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2501.05895

Abstract

Let G be a locally compact second countable groupoid with a fixed Haar system λ=\λ^u\_{u∈ G⁰} and (Φ,Ψ) be a complementary pair of N-functions satisfying Δ₂-condition. In this article, we introduce the continuous field of Orlicz space (L^Φ₀,Δ₁) and provide a sufficient condition for the space of continuous sections vanishing at infinity, denoted E^Φ₀, to be an Banach algebra under a suitable convolution. Further, the condition for a closed C_b(G⁰)-submodule I of E^Φ₀ to be a left ideal is established. Moreover, we provide a groupoid analogue of the characterization of the space of convolutors of Morse-Transue space for locally compact groups.

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