Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups

• Autorzy: Nageswaran Shravan Kumar
• Języki publikacji: EN

Abstrakty

EN

Let K be an ultraspherical hypergroup associated to a locally compact group G and a spherical projector π and let VN(K) denote the dual of the Fourier algebra A(K) corresponding to K. In this note, invariant means on VN(K) are defined and studied. We show that the set of invariant means on VN(K) is nonempty. Also, we prove that, if H is an open subhypergroup of K, then the number of invariant means on VN(H) is equal to the number of invariant means on VN(K). We also show that a unique topological invariant mean exists precisely when K is discrete. Finally, we show that the set TIM(K̂) becomes uncountable if K is nondiscrete.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 46J10: Banach algebras of continuous functions, function algebras
• 43A62: Hypergroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 225
• Numer: 3
• Strony: 235-247

Daty

wydano

2014

Twórcy

autor

Nageswaran Shravan Kumar

• Department of Mathematics, Indian Institute of Technology Delhi, Delhi 110016, India

Identyfikatory

DOI

10.4064/sm225-3-4