2012/08/23 by Mahya Ghandehari, Hun Hee Lee, Ghandehari, Mahya +5
Mathematics · #47L25 Secondary 43A75 #47L30 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 43A30
paper · pdf · doi:10.48550/arxiv.1208.4835
openalex publication_date 2012/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a compact connected Lie group. The question of when a weighted Fourier algebra on G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G with the order of growth strictly bigger than the half of the dimension of the group. The case of SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.