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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |