On Gelfand-Mazur theorem on a class ofF-algebras

• Autorzy: E. Anjidani
• Języki publikacji: EN

Abstrakty

EN

A topological algebra A is said to be fundamental if there exists b > 1 such that for every sequence (xn) in A, (xn) is Cauchy whenever the sequence bn(xn − xn-1) tends to zero as n → ∞. Let A be a complex unital fundamental F-algebra with bounded elements such that A* separates the points on A. Then we prove that the spectrum σ(a) of every element a ∈ A is nonempty compact. Moreover, if A is a division algebra, then A is isomorphic to the complex numbers ℂ. This result is a generalization of Gelfand-Mazur theorem for a large class of F-algebras, containing both locally bounded algebras and locally convex algebras with bounded elements.

Słowa kluczowe

EN

Gelfand-Mazur theorem; F-algebra; fundamental topological algebra; topological algebra withbounded elements; division algebra

Kategorie tematyczne

• 46H20: Structure, classification of topological algebras
• 46H05: General theory of topological algebras

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2013-04-11

zaakceptowano

2014-04-01

online

2014-08-08

Twórcy

autor

E. Anjidani

• Department of Mathematics, University of Neyshabur, P.O.Box 91136-899, Neyshabur, Iran

Bibliografia

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Identyfikatory

DOI

10.2478/taa-2014-0004