P-Amenable Locally Compact Hypergroups

Author:
,
Year
: 2006
Abstract: Abstract. Let K be a locally compact hypergroup with left Haar

measure and let P1

(K) = {f ∈ L1

(K) : f ≥ 0, kfk1 = 1 }. Then

P1

(K) is a topological semigroup under the convolution product of

L1

(K) induced in P1

(K). We say that K is P-amenable if there

exists a left invariant mean on C(P1

(K)), the space of all bounded

continuous functions on P1

(K). In this note, we consider the P-

amenability of hypergroups. The P-amenability of hypergroup joins

K = H ∨ J where H is a compact hypergroup and J is a discrete

hypergroup with H∩J = {e} is characterized. It is also shown that

Z-hypergroups are P-amenable if Z(K) ∩ G(K) is compact
Keyword(s): Hypergroup,Left invariant mean,Amenable,P-amenable,Hypergroup joins,Zhypergroup,Strongly normal,Supernormal,Topological semigroup
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