A note on κ-uniform points of $G^{\mathcal{LUC}}$

Alaste, T.

doi:10.1007/s00233-013-9482-y

Cited by 3 publications

(3 citation statements)

References 3 publications

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“…Since [p] is a closed left ideal of G LU C for every p ∈ ϕ, we always have |π(ϕ)| ≤ 2 2 κ (see, for example, [14]). Recall that U(G) = ϕ κ is an ideal of G LU C (see [2]). Therefore, the assumption ϕ κ ⊆ ϕ in the next theorem implies ϕ ⊆ ϕ κ = U(G).…”

Section: Semigroup Compactifications Of G Containing Right Zerosmentioning

confidence: 99%

On the spectra of C⁎-algebras of slowly oscillating functions on locally compact groups

Alaste

Filali

2015

Advances in Mathematics

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We present a study of C * -algebras SO(ϕ) of slowly oscillating functions in the direction of filters ϕ on a locally compact topological group G. We show that SO(ϕ) is an m-admissible subalgebra of C(G) if and only if the closure of the filter ϕ in the LU C-compactification G LU C of G is an ideal of G LU C and that the semigroup compactification of G determined by SO(ϕ) always contains right zero elements. Using this, we characterize a new interesting C * -algebra of bounded continuous functions on G. The spectrum of this C * -algebra determines the universal semigroup compactification of G with respect to the property that the semigroup compactification contains a right zero element. We show that the topological center of this universal compactification is G. As an application of the previous results, we show that every closed ideal of G LU C contained in the ideal U (G) of uniform points of G LU C can be decomposed into 2 2 κ(G) closed left ideals of G LU C .

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Section: Semigroup Compactifications Of G Containing Right Zerosmentioning

confidence: 99%

On the spectra of C⁎-algebras of slowly oscillating functions on locally compact groups

Alaste

Filali

2015

Advances in Mathematics

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“…All semigroup compactifications of a semitopological semigroup as a collection of z-ultrafilters or e-ultrafilters have been described, see [1], [2], [3] and [4] for more details and some applications. This approach gives us a new light on studying this kind of compactifications.…”

Section: Introductionmentioning

confidence: 99%

“…This approach gives us a new light on studying this kind of compactifications. It seems that the methods presented in [1], [2], [3] and [4] can serve as a valuable tool in the study of semigroup compactifications and also of topological compactifications. But this methods depend on concepts of topology on semigroups.…”

Section: Introductionmentioning

confidence: 99%

Ultrafilters on measurable semigroups

Pashapournia,

Tootkaboni,

Ebrahimbagha

2019

Preprint

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Let (S, •) be a semigroup and m be a σ-algebra on S. We say (S, •, m) is a measurable semigroup if π : S × S −→ S by π(x, y) = x • y is a measurable function. In this paper , we consider to m β as the collection of all ultrafilters on m. We show that m β is a compact right topological semigroup respect to generated topology by σ-algebra m on m β . Also we study some elementary properties of the algebraic structure of m β .

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Filters on topological groups

Alaste

2014

Semigroup Forum

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A note on κ-uniform points of $G^{\mathcal{LUC}}$

Cited by 3 publications

References 3 publications

On the spectra of C⁎-algebras of slowly oscillating functions on locally compact groups

On the spectra of C⁎-algebras of slowly oscillating functions on locally compact groups

Ultrafilters on measurable semigroups

Filters on topological groups

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