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.
Unit laws are others.
Not commutativity.
How about von Neuman quasi-inverse identities
x x+ x =
x?
F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus