Vol. 80, No. 1, 1979

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Spectral synthesis in Segal algebras on hypergroups

Ajit Kaur Chilana and Ajay Kumar

Vol. 80 (1979), No. 1, 59–76

Warner (1966), Hewitt and Ross (1970), Yap (1970), and Yap (1971) extended the so-called Ditkin’s condition for the group algebra L1(G) of a locally compact abelian group G to the algebras L1(G) L2(G), dense subalgebras of L1(G) which are essential Banach L1(G)-modules, L1(G) Lp(G)(1 p < ) and Segal algebras respectively. Chilana and Ross (1978) proved that the algebra L1(K) satisfies a stronger form of Ditkin’s condition at points of the center Z(K) of K, where K is a commutative locally compact hypergroup such that its dual K is also a hypergroup under pointwise operations. Topological hypergroups have been defined and studied by Dunkl (1973), Spector (1973), and Jewett (1975) to begin with. In this paper we define Segal algebras on K and prove that they satisfy a stronger form of Ditkin’s condition at the points of Z(K). Examples include the analogues of some Segal algebras on groups and their intersections.

Mathematical Subject Classification 2000
Primary: 43A45
Received: 16 February 1978
Revised: 10 April 1978
Published: 1 January 1979
Ajit Kaur Chilana
Ajay Kumar