Topological spectrum of elements in topological algebras

Abel, Mati; Zárate-Rodríguez, Yuliana de Jesús

doi:10.3176/proc.2018.3.05

Cited by 2 publications

(2 citation statements)

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“…Indeed, Abel provided a characterization of topological algebras in which the set of topologically quasi-invertible elements coincides with the set of quasi-invertible elements. Recently, Abel and Zárate-Rodríguez [2] studied the properties of left, right, and two-sided topologically quasi-invertible elements showing that all these sets are G δ -sets in F-algebras A. The previous result in a unital algebra A can be written as TopQInv r (A) = {e}−TopInv r (A).…”

Section: Proposition 27 An Element X In a Unital Normed Algebra A Is ...mentioning

confidence: 99%

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Approximately invertible elements in non-unital normed algebras

Esmeral¹,

Feichtinger²,

Hutník³

et al. 2021

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We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct extension of topological invertibility to non-unital algebras. Basic observations relate approximate invertibility with concepts of topological divisors of zero and density of (modular) ideals. We exemplify approximate invertibility in the group algebra, Wiener algebras, and operator ideals. For Wiener algebras with approximate identities (in particular, for the Fourier image of the convolution algebra), the approximate invertibility of an algebra element is equivalent to the property that it does not vanish. We also study approximate invertibility and its deeper connection with the Gelfand and representation theory in non-unital abelian Banach algebras as well as abelian and non-abelian C*-algebras. MSC (2020): 46H10, 46L05, 43A20.

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Section: Proposition 27 An Element X In a Unital Normed Algebra A Is ...mentioning

confidence: 99%

“…Recent Abel results on sets of topologically quasi-invertible sets, see [2], motivate further research on the structure of the sets of AppInv ℓ (A) and AppInv r (A) in A. For instance, for which algebras A are these sets G δ -sets?…”

Section: An Application To the Density In Banach Modulesmentioning

confidence: 99%