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1. CMB Online first
A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability |
A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability In this paper we present a fixed point property for amenable
hypergroups which is analogous to Rickert's fixed point theorem
for semigroups. It equates the existence of a left invariant
mean on the space of weakly right uniformly continuous functions
to the existence of a fixed point for any action of the hypergroup.
Using this fixed point property, a certain class of hypergroups
are shown to have a left Haar measure.
Keywords:invariant measure, Haar measure, hypergroup, amenability, function translations Categories:43A62, 43A05, 43A07 |
2. CMB 2012 (vol 57 pp. 37)
Character Amenability of Lipschitz Algebras Let ${\mathcal X}$ be a locally compact metric space and let
${\mathcal A}$ be any of the Lipschitz algebras
${\operatorname{Lip}_{\alpha}{\mathcal X}}$, ${\operatorname{lip}_{\alpha}{\mathcal X}}$ or
${\operatorname{lip}_{\alpha}^0{\mathcal X}}$. In this paper, we show, as a
consequence of rather more general results on Banach algebras,
that ${\mathcal A}$ is $C$-character amenable if and only if
${\mathcal X}$ is uniformly discrete.
Keywords:character amenable, character contractible, Lipschitz algebras, spectrum Categories:43A07, 46H05, 46J10 |
3. CMB 2008 (vol 51 pp. 60)
F{\o}lner Nets for Semidirect Products of Amenable Groups For unimodular semidirect products of locally compact amenable
groups $N$ and $H$, we show that one can always construct a
F{\o}lner net of the form $(A_\alpha \times B_\beta)$ for $G$, where
$(A_\alpha)$ is a strong form of F{\o}lner net for $N$ and
$(B_\beta)$ is any F{\o}lner net for $H$. Applications to the
Heisenberg and Euclidean motion groups are provided.
Categories:22D05, 43A07, 22D15, 43A20 |
4. CMB 2001 (vol 44 pp. 231)
Weak Convergence Is Not Strong Convergence For Amenable Groups Let $G$ be an infinite discrete amenable group or a non-discrete
amenable group. It is shown how to construct a net $(f_\alpha)$ of
positive, normalized functions in $L_1(G)$ such that the net converges weak*
to invariance but does not converge strongly to invariance. The solution of
certain linear equations determined by colorings of the Cayley graphs of the
group are central to this construction.
Category:43A07 |