A Note on Commuting Powers in Banach Algebras
نویسنده
چکیده
If m is a positive integer, let ǫk = e 2kπi/m for k = 1, . . . ,m. Then ǫk = 1 (k = 1, . . . ,m), ǫk 6= 1 (k = 1, . . . ,m− 1) and ǫm = 1 . If a ∈ A is invertible, define the bounded linear operator Ta : A → A by Tax = a xa (x ∈ A) . Proposition 1. Suppose that a ∈ A is invertible, m is a positive integer and that σ(a) is irrotational (mod 2π/m). Let the bounded linear operator S : A → A be given by
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