A theorem of Gel'fand-Mazur type

• Autorzy: Hung Le Pham
• Języki publikacji: EN

Abstrakty

EN

Denote by 𝔠 any set of cardinality continuum. It is proved that a Banach algebra A with the property that for every collection ${a_{α}: α ∈ 𝔠} ⊂ A$ there exist α ≠ β ∈ 𝔠 such that $a_{α} ∈ a_{β}A^{#}$ is isomorphic to
$⨁_{i=1}^{r} (ℂ[X]/X^{d_{i}}ℂ[X]) ⊕ E$,
where $d₁,...,d_{r} ∈ ℕ$, and E is either $Xℂ[X]/X^{d₀}ℂ[X]$ for some d₀ ∈ ℕ or a 1-dimensional $⨁_{i=1}^{r} ℂ[X]/X^{d_{i}}ℂ[X]$-bimodule with trivial right module action. In particular, ℂ is the unique non-zero prime Banach algebra satisfying the above condition.

Kategorie tematyczne

• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 1
• Strony: 81-88

Daty

wydano

2009

Twórcy

autor

Hung Le Pham

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Identyfikatory

DOI

10.4064/sm191-1-6