Regularities and subspectra for commutative Banach algebras
نویسندگان
چکیده
The set G(B) of invertible elements of B is the main example of a regularity. As was proved in [4], the set of elements of B which are not topological zero divisors is also a regularity. In the present paper, we investigate a construction of joint spectra in B by means of regularities in B. Let σ(a)= {μ∈ C | a−μe ∈G(B)} be the ordinary spectrum in B. Recall that according to the terminology introduced by Żelazko [6], a subspectrum τ in B is a mapping which associates to every k-tuple (a1, . . . ,ak)∈ Bk a nonempty compact set τ(a1, . . . ,ak) such that (a) τ(a1, . . . ,ak)⊂ ∏k i=1 σ(ai), (b) τ(p(a1, . . . ,ak))= p(τ(a1, . . . ,ak)) for every polynomialmapping p = (p1, . . . , pm) : Ck → Cm. In Theorem 2.1, we prove that an arbitrary subspectrum τ in B defines a regularity Rτ by the formula Rτ = { a∈ B | 0 ∈ τ(a)}. (1.3)
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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005