Joint Spectra of Generators in Topological Algebras
2007 ◽
Vol 2007
◽
pp. 1-7
Keyword(s):
Let𝒜be a complex topological algebra with unit 1 and𝒰a family of proper closed ideals in𝒜. For an arbitraryS⊂𝒜we define a globally defined joint spectrumσ𝒰(S)={(λs)s∈S∈ℂS | ∃ I ∈𝒰(s−λs)∈I ∀s∈S}. We prove that forSgenerating𝒜the spectrumσ𝒰(S)can be identified with the set𝔐𝒰of continuous multiplicative functionalsfon𝒜such that kerf∈𝒰. The relation is given by the formulaσ𝒰(S)={(f(s))s∈S | f∈𝔐𝒰}. If𝒜is aQ-algebra, the setσ𝒰(S)is rationally convex.
1977 ◽
Vol 17
(3)
◽
pp. 391-399
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2014 ◽
Vol 66
(1)
◽
pp. 205-240
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1972 ◽
Vol 6
(2)
◽
pp. 161-167
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2020 ◽
Vol 24
(1)
◽
pp. 147-158
Keyword(s):
1979 ◽
Vol 22
(4)
◽
pp. 413-418
◽
Keyword(s):
1969 ◽
Vol 1
(3)
◽
pp. 419-424
◽
Keyword(s):