Bulletin of the Iranian Mathematical Society, ( ISI ), Volume (32), No (2), Year (2006-3) , Pages (43-51)

Title : P-AMENABLE LOCALLY COMPACT HYPERGROUPS ( P-Amenable Locally Compact Hypergroups )

Authors: Rajab Ali Kamyabi Gol ,

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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

Keywords

, Hypergroup; Left invariant mean; Amenable; P, amenable; Hypergroup joins; Zhypergroup; Strongly normal; Supernormal; Topological
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@article{paperid:203387,
author = {Kamyabi Gol, Rajab Ali},
title = {P-AMENABLE LOCALLY COMPACT HYPERGROUPS},
journal = {Bulletin of the Iranian Mathematical Society},
year = {2006},
volume = {32},
number = {2},
month = {March},
issn = {1735-8515},
pages = {43--51},
numpages = {8},
keywords = {Hypergroup; Left invariant mean; Amenable; P-amenable; Hypergroup joins; Zhypergroup; Strongly normal; Supernormal; Topological semigroup},
}

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%0 Journal Article
%T P-AMENABLE LOCALLY COMPACT HYPERGROUPS
%A Kamyabi Gol, Rajab Ali
%J Bulletin of the Iranian Mathematical Society
%@ 1735-8515
%D 2006

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