C.M.S. • Fredericton, NB • June 2010
Meditations on Arens Multiplication
   F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus

  Problems: 1) (in Ban₁) Which Banach algebras A have A** commutative?
2) What other symmetric (and closed ?) monoidal categories have interesting dualizing objects C? For which is ** symmetric? Or, at least, for which will commutative monoid A have A** commutative? A topos, and C = Ω? AbGp, and C = the circle group? Posets? Simplicial sets? Topological spaces? R-modules? For what C?
3) The ‡ procedure endows A** with a counterpart to each finitary ⊗-operation ⊗ⁿA → A an algebra A may have, and associativity is one equation that A** inherits.