Author:
Ebrahimzadeh Esfahani Ali,Nemati Mehdi,Ghanei Mohammad Reza
Abstract
AbstractLet
${\mathcal A}$
be a Banach algebra, and let
$\varphi $
be a nonzero character on
${\mathcal A}$
. For a closed ideal I of
${\mathcal A}$
with
$I\not \subseteq \ker \varphi $
such that I has a bounded approximate identity, we show that
$\operatorname {WAP}(\mathcal {A})$
, the space of weakly almost periodic functionals on
${\mathcal A}$
, admits a right (left) invariant
$\varphi $
-mean if and only if
$\operatorname {WAP}(I)$
admits a right (left) invariant
$\varphi |_I$
-mean. This generalizes a result due to Neufang for the group algebra
$L^1(G)$
as an ideal in the measure algebra
$M(G)$
, for a locally compact group G. Then we apply this result to the quantum group algebra
$L^1({\mathbb G})$
of a locally compact quantum group
${\mathbb G}$
. Finally, we study the existence of left and right invariant
$1$
-means on
$ \operatorname {WAP}(\mathcal {T}_{\triangleright }({\mathbb G}))$
.
Publisher
Canadian Mathematical Society
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