2009/04/04 by Osvaldo Osuna Castro, Castro, Osvaldo Osuna, Elmar Wagner +1
Mathematics · #17B37 #47L60 #81R50 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Random Matrices and Applications #math.OA #math.QA #msc:17B37 #msc:47L60 #msc:81R50
paper · pdf · doi:10.48550/arxiv.0904.0669
16 pages
arxiv created 2009/04/04 · openalex publication_date 2009/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do not admit bounded Hilbert space representations and their self-adjoint generators have continuous spectrum. Operator algebras of trace class operators are associated to the coordinate algebras which allow interpretations as rapidly decreasing functions and as finite functions. The invariant integral is defined as a trace functional which generalizes the well-known quantum trace. We argue that previous algebraic methods would fail for these examples.