Hemi-Multiplicative Operators and Related Operators in Finite-Dimensional Algebras
Hermitian powers: A Müntz theorem and extremal algebras
Given ⊂ ℕ, let ̂ be the set of all positive integers m for which is hermitian whenever h is an element of a complex unital Banach algebra A with hⁿ hermitian for each n ∈ . We attempt to characterize when (i) ̂ = ℕ, or (ii) ̂ = . A key tool is a Müntz-type theorem which gives remarkable conclusions when 1 ∈ and ∑ 1/n: n ∈ diverges. The set ̂ is determined by a single extremal Banach algebra Ea(). We describe this extremal algebra for various .
Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras.