Abstract
Let
$(G_1,\omega _1)$
and
$(G_2,\omega _2)$
be weighted discrete groups and
$0\lt p\leq 1$
. We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra
$\ell ^p(G_1,\omega _1)$
. We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras
$\ell ^p(G_1,\omega _1)$
and
$\ell ^p(G_2,\omega _2)$
and isometric algebra isomorphisms between
$\ell ^p(S_1,\omega _1)$
and
$\ell ^p(S_2,\omega _2)$
, where
$(S_1,\omega _1)$
and
$(S_2,\omega _2)$
are weighted discrete semigroups.
Module character inner amenability of Banach algebras