Joint Spectra of Generators in Topological Algebras
Let 𝒜 be a complex topological algebra with unit 1 and 𝒰 a family of proper closed ideals in 𝒜. For an arbitrary S⊂𝒜 we define a globally defined joint spectrum σ𝒰(S)={(λs)s∈S∈ℂS | ∃ I ∈𝒰(s−λs)∈I ∀s∈S}. We prove that for S generating 𝒜 the spectrum σ𝒰(S) can be identified with the set 𝔐𝒰 of co...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/96289 |
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| author | Antoni Wawrzyńczyk |
| author_facet | Antoni Wawrzyńczyk |
| author_sort | Antoni Wawrzyńczyk |
| collection | DOAJ |
| description | Let 𝒜 be a complex topological algebra with unit 1 and 𝒰 a
family of proper closed ideals in 𝒜. For an arbitrary
S⊂𝒜 we define a globally defined joint spectrum
σ𝒰(S)={(λs)s∈S∈ℂS | ∃ I ∈𝒰(s−λs)∈I ∀s∈S}. We prove that for S generating 𝒜 the spectrum σ𝒰(S) can be identified with the set 𝔐𝒰 of
continuous multiplicative functionals f on 𝒜 such that ker f∈𝒰. The relation is given by the formula
σ𝒰(S)={(f(s))s∈S | f∈𝔐𝒰}. If 𝒜 is a Q-algebra, the set σ𝒰(S) is rationally convex. |
| format | Article |
| id | doaj-art-8244b498c0dc4a2d8ddc5f929298fca9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8244b498c0dc4a2d8ddc5f929298fca92025-02-03T01:30:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/9628996289Joint Spectra of Generators in Topological AlgebrasAntoni Wawrzyńczyk0Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenue San Rafael Atlixco 186, Col. Vicentina, AP 55-534, México 09340, DF, MexicoLet 𝒜 be a complex topological algebra with unit 1 and 𝒰 a family of proper closed ideals in 𝒜. For an arbitrary S⊂𝒜 we define a globally defined joint spectrum σ𝒰(S)={(λs)s∈S∈ℂS | ∃ I ∈𝒰(s−λs)∈I ∀s∈S}. We prove that for S generating 𝒜 the spectrum σ𝒰(S) can be identified with the set 𝔐𝒰 of continuous multiplicative functionals f on 𝒜 such that ker f∈𝒰. The relation is given by the formula σ𝒰(S)={(f(s))s∈S | f∈𝔐𝒰}. If 𝒜 is a Q-algebra, the set σ𝒰(S) is rationally convex.http://dx.doi.org/10.1155/2007/96289 |
| spellingShingle | Antoni Wawrzyńczyk Joint Spectra of Generators in Topological Algebras International Journal of Mathematics and Mathematical Sciences |
| title | Joint Spectra of Generators in Topological Algebras |
| title_full | Joint Spectra of Generators in Topological Algebras |
| title_fullStr | Joint Spectra of Generators in Topological Algebras |
| title_full_unstemmed | Joint Spectra of Generators in Topological Algebras |
| title_short | Joint Spectra of Generators in Topological Algebras |
| title_sort | joint spectra of generators in topological algebras |
| url | http://dx.doi.org/10.1155/2007/96289 |
| work_keys_str_mv | AT antoniwawrzynczyk jointspectraofgeneratorsintopologicalalgebras |