Homomorphisms on algebras of analytic functions on non-symmetrically regular spaces

Abstract: We study homomorphisms on the algebra of analytic functions of bounded type on a Banach space. When the domain space lacks symmetric regularity, we show that in every fiber of the spectrum there are evaluations (in higher duals) which do not coincide with evaluations in the second dual. We also consider the commutativity of convolutions between evaluations. We show that in some Banach spaces $X$ (for example, $X=\ell_1$) the only evaluations that commute with every other evaluation in $X''$ are those in $X$. Finally, we establish conditions ensuring the symmetry of the canonical extension of a symmetric multilinear operator (on a non-symmetrically regular space) and present some applications.