Harmonic operators on convolution quantum group algebras

2024/05/17 by Mehdi Nemati, Nemati, Mehdi, Sima Soltani Renani +1
Mathematics · #22D15 #43A07 #43A22 #46H05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2405.10910

openalex publication_date 2024/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Bbb G be a locally compact quantum group and \mathcal T(L²(\Bbb G)) be the Banach algebra of trace class operators on L²(\Bbb G) with the convolution induced by the right fundamental unitary of \Bbb G. We study the space of harmonic operators \widetilde\mathcal H_ω in \mathcal B(L²(\Bbb G)) associated to a contractive element ω∈ \mathcal T(L²(\Bbb G)). We characterize the existence of non-zero harmonic operators in \mathcal K(L²(\Bbb G)) and relate them with some properties of the quantum group \Bbb G, such as finiteness, amenability and co-amenability.

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