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Hermitian powers: A Müntz theorem and extremal algebras

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Crabb M., Duncan J., McGregor C., Ransford T.

Studia Mathematica

2001

tom 146

nr 1

83-97

Given 𝕊 ⊂ ℕ, let 𝕊̂ be the set of all positive integers m for which $h^{m}$ is hermitian whenever h is an element of a complex unital Banach algebra A with hⁿ hermitian for each n ∈ 𝕊. We attempt to characterize when (i) 𝕊̂ = ℕ, or (ii) 𝕊̂ = 𝕊. A key tool is a Müntz-type theorem which gives remarkable conclusions when 1 ∈ 𝕊 and ∑ {1/n: n ∈ 𝕊} diverges. The set 𝕊̂ is determined by a single extremal Banach algebra Ea(𝕊). We describe this extremal algebra for various 𝕊.

Ograniczanie wyników

1 Studia Mathematica

1 Crabb M.

1 Duncan J.

1 McGregor C.

1 Ransford T.

1 2001

Wyniki wyszukiwania

Hermitian powers: A Müntz theorem and extremal algebras