  Let ${\mathcal A}$ be a Banach algebra and let $\varphi $ be a non-zero
character on ${\mathcal A}$. Suppose that ${\mathcal A}_M$ is the closure of
the faithful Banach algebra ${\mathcal A}$ in the multiplier norm. In this
paper, topologically left invariant $\varphi$-means on ${\mathcal A}_M^*$ are
defined and studied. Under some conditions on ${\mathcal A}$, we will show that
the set of topologically left invariant $\varphi$-means on ${\mathcal A}^*$ and
on ${\mathcal A}_M^*$ have the same cardinality. We also study the left
uniformly continuous functionals associated with these algebras. The main
applications are concerned with the Fourier algebra of an ultraspherical
hypergroup $H$. In particular, we obtain some characterizations of discreteness
of $H$.
