# On Gelfand-Mazur theorem on a class of F -algebras

Topological Algebra and its Applications (2014)

- Volume: 2, Issue: 1, page 19-23, electronic only
- ISSN: 2299-3231

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topE. Anjidani. " On Gelfand-Mazur theorem on a class of F -algebras ." Topological Algebra and its Applications 2.1 (2014): 19-23, electronic only. <http://eudml.org/doc/266794>.

@article{E2014,

abstract = {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.},

author = {E. Anjidani},

journal = {Topological Algebra and its Applications},

keywords = {Gelfand-Mazur theorem; F-algebra; fundamental topological algebra; topological algebra with
bounded elements; division algebra; -algebra; topological algebra with bounded elements; fundamental algebra; dual separating the points},

language = {eng},

number = {1},

pages = {19-23, electronic only},

title = { On Gelfand-Mazur theorem on a class of F -algebras },

url = {http://eudml.org/doc/266794},

volume = {2},

year = {2014},

}

TY - JOUR

AU - E. Anjidani

TI - On Gelfand-Mazur theorem on a class of F -algebras

JO - Topological Algebra and its Applications

PY - 2014

VL - 2

IS - 1

SP - 19

EP - 23, electronic only

AB - 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.

LA - eng

KW - Gelfand-Mazur theorem; F-algebra; fundamental topological algebra; topological algebra with
bounded elements; division algebra; -algebra; topological algebra with bounded elements; fundamental algebra; dual separating the points

UR - http://eudml.org/doc/266794

ER -

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