65 research outputs found
Right cancellation, factorization, and right isometries
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A key tool in the study of the strong Arens irregularity of Banach algebras in harmonic analysis comes in form of right cancellation, factorization, and right isometries. In this paper, we show that these are in many cases the same.Abstract
A key tool in the study of the strong Arens irregularity of Banach algebras in harmonic analysis comes in form of right cancellation, factorization, and right isometries. In this paper, we show that these are in many cases the same
A Look at the Condition of Women in Malentendues by Azza Filali
No full textA Look at the Female Condition in Malentendues by Azza Filali
This article analyzes the female condition through the central character of Malentendus by Azza Filali. It explores the tensions between social injunctions and individual aspirations, highlighting how the author constructs a female figure striving for emancipation in a Tunisian context marked by deep contradictions. The study examines the narrative and discursive strategies that reveal the obstacles, resistances, and ambiguities shaping the character’s journey. Adopting a literary and socio-critical approach, this article investigates the representation of power dynamics and identity issues in the novelCe travail propose une analyse de la condition féminine à travers le personnage central de Malentendues d’Azza Filali. Il s’agit d’explorer les tensions entre injonctions sociales et aspirations individuelles, mettant en avant la manière dont la romancière présente une figure féminine en quête d’émancipation dans un contexte tunisien marqué par des contradictions majeures. L’article examine les stratégies narratives et discursives qui révèlent les obstacles, les résistances et les ambiguïtés du parcours de ce personnage. En adoptant une approche sociocritique, ce travail interroge la représentation des rapports de pouvoir et des dynamiques identitaires à l’œuvre dans le roman
Interpolation sets and the size of quotients of function spaces on a locally compact group
Get PDFWe devise a fairly general method for estimating the size of quotients between algebras of functions on a locally compact group. This method is based on the concept of interpolation sets and unifies the approaches followed by many authors to obtain particular cases.
Among the applications we find, we obtain that the quotients WAP(G)/B(G) (G being a locally compact group in the class [IN] or a nilpotent locally compact group) and CB(G)/LUC(G) (G being any non-compact non-discrete locally compact group) contain a linearly isometric copy of \ell_\infty(\kappa(G)) where \kappa(G) is the compact covering number of G, and WAP(G), B(G) and LUC(G) refer, respectively, to the algebra of weakly almost periodic functions, the uniform closure of the Fourier-Stieltjes algebra and the bounded right uniformly continuous functions.The research of the second author was partially supported by the Spanish Ministry of Science (including FEDER funds), grant MTM2011-23118 and Fundació Caixa Castelló-Bancaixa, grant number P11B2014-35
1Kernels of bounded operators on the classical transfinite Banach sequence spaces
No full textEvery closed subspace of each of the Banach spaces X = ℓ p ( Γ ) and X = c 0 ( Γ ) , where Γ is a set and 1 < p < ∞ , is the kernel of a bounded operator X → X . On the other hand, whenever Γ is an uncountable set, ℓ 1 ( Γ ) contains a closed subspace that is not the kernel of any bounded operator ℓ 1 ( Γ ) → ℓ 1 ( Γ )
Subspaces that can and cannot be the kernel of a bounded operator on a Banach space
Get PDFGiven a Banach space E, we ask which closed subspaces may be realised as the kernel of a bounded operator E→E. We prove some positive results which imply in particular that when E is separable every closed subspace is a kernel. Moreover, we show that there exists a Banach space E which contains a closed subspace that cannot be realised as the kernel of any bounded operator on E. This implies that the Banach algebra B(E) of bounded operators on E fails to be weak*-topologically left Noetherian in the sense of (JT White, Left Ideals of Banach Algebras and Dual Banach Algebras, preprint, 2018). The Banach space E that we use is the dual of one of Wark’s non-separable, reflexive Banach spaces with few operators
Towards a sheaf cohomology theory for C*-algebras
No full textIn joint work with Pere Ara (Barcelona) we are in the process of developing a full sheaf cohomology theory for noncommutative C*-algebras. In this survey, we discuss the difficulties arising from the fact that the appropriate categories of operator module sheaves over sheaves of C*-algebras are non-abelian and therefore the homology theory needed has to be set in the more general framework of exact categories
Kernels of bounded operators on the classical transfinite Banach sequence spaces
Get PDFEvery closed subspace of each of the Banach spaces X=lp(Γ) and X=c0(Γ), where Γ is a set and 1<p<∞, is the kernel of a bounded operator X→X. On the other hand, whenever Γ is an uncountable set, l1(Γ) contains a closed subspace that is not the kernel of any bounded operator l1(Γ)→l1(Γ)
Subspaces that can and cannot be the kernel of a bounded operator on a Banach space
No full textGiven a Banach space E, we ask which closed subspaces may be realized as the kernel of a bounded operator E → E . We prove some positive results, which imply in particular that when E is separable every closed subspace is a kernel. Moreover, we show that there exists a reflexive Banach space E which contains a closed subspace that cannot be realized as the kernel of any bounded operator on E. This implies that the Banach algebra of bounded operators on E fails to be weak ∗ -topologically left Noetherian in the sense of [7]. The Banach space E that we use is the dual of one of Wark’s non-separable, reflexive Banach spaces with few operators
Relations between ideals of the figa-Talamanca herz algebra A<inf>p</inf>(G) of a locally compact group G and ideals of A<inf>p</inf>(H) of a closed subgroup
No full textLet G be a locally compact group and H a closed subgroup. In analogy with the classical case,we obtain the two following results. Suppose at first that G is amenable and that I is a closed ideal of Ap (H) having a bounded approximate unit, then the ideal {u € Ap(G)|Reshu €I} of Ap(G) also has a bounded approximate unit. The second result concerns the closedness of { Reshu €I I} in Ap(H) for a closed ideal I of Ap(G). We show that this set is closed if H is amenable.PH-S
Towards a sheaf cohomology theory for C<sup>*</sup>-algebras
No full textIn joint work with Pere Ara (Barcelona), we are in the process of develop-ing a full sheaf cohomology theory for noncommutative C*-algebras. In this survey, we discuss the difficulties arising from the fact that the appropriate categories of operator module sheaves over sheaves of C*-algebras are non-Abelian and, therefore, the homol- ogy theory needed has to be set in the more general framework of exact categories.</p
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