Hermitian powers: A Müntz theorem and extremal algebras

• Autorzy: M. J. Crabb , J. Duncan , C. M. McGregor , T. J. Ransford
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 146
• Numer: 1
• Strony: 83-97

Daty

wydano

2001

Twórcy

autor

M. J. Crabb

• Department of Mathematics, University of Glasgow, Glasgow G12 8QW, U.K.

autor

J. Duncan

• Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701-1201, U.S.A.

autor

C. M. McGregor

• Department of Mathematics, University of Glasgow, Glasgow G12 8QW, U.K.

autor

T. J. Ransford

• Department of Mathematics and Statistics, Laval University, Québec, Canada G1K 7P4

Identyfikatory

DOI

10.4064/sm146-1-6