Countable linear combinations of characters on commutative Banach algebras
Feinstein, J. F.
Original · EN
An elegant but elementary result of Wolff from 1921, when interpreted in terms of Banach algebras, shows that it is possible to find a sequence of distinct characters ϕₙ on the disc algebra and an ℓ₁ sequence of complex numbers λₙ, not all zero, such that ∑ₙ₌₁∞ λₙ ϕₙ =0. We observe that, even for general commutative, unital Banach algebras, this is not possible if the closure of the countable set of characters has no perfect subsets.
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