The free Banach f-algebra FBfA[E] is constructed with a C(B_E*) representation that is injective on completion precisely when semiprime, which holds for finite-dimensional E or E = L1(μ), plus an extension theorem for real lattice-algebra homomorphisms from closed sublattice-algebras.
On Wigner’s theorem in smooth normed spaces
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Free Banach $f$-algebras
The free Banach f-algebra FBfA[E] is constructed with a C(B_E*) representation that is injective on completion precisely when semiprime, which holds for finite-dimensional E or E = L1(μ), plus an extension theorem for real lattice-algebra homomorphisms from closed sublattice-algebras.