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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
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
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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