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

100%

Shravan Kumar N.

Studia Mathematica

2014

tom 225

nr 3

235-247

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.

Ditkin sets in homogeneous spaces

63%

Parthasarathy K., Shravan Kumar N.

Studia Mathematica

2011

tom 203

nr 3

291-307

Ditkin sets for the Fourier algebra A(G/K), where K is a compact subgroup of a locally compact group G, are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are also given.

Ograniczanie wyników

2 Studia Mathematica

2 Shravan Kumar N.

1 Parthasarathy K.

1 2014

1 2011

Wyniki wyszukiwania

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

Ditkin sets in homogeneous spaces