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|Type:||Artigo de periódico|
|Title:||On Biorthogonal Systems Whose Functionals Are Finitely Supported|
|Abstract:||We show that for each natural number n > 1, it is consistent that there is a compact Hausdorff totally disconnected space K2n such that C(K2n) has no uncountable (semi)biorthogonal sequence (f ψ,μψ)ψ∈ω1 where μψ's are atomic measures with supports consisting of at most 2n..1 points of K2n, but has biorthogonal systems (fφ, μφ)φ∈ω1 where μψ's are atomic measures with supports consisting of 2n points. This complements a result of Todorcevic which implies that it is consistent that such spaces do not exist: he proves that its is consistent that for any nonmetrizable compact Hausdorff totally disconnected space K, the Banach space C(K) has an uncountable biorthogonal system where the functionals are measures of the form δxψ - δyψ for ψ < ω1 and xψ yψ ∈ K. It also follows from our results that it is consistent that the irredundance of the Boolean algebra Clop(K) for a totally disconnected K or of the Banach algebra C(K) can be strictly smaller than the sizes of biorthogonal systems in C(K). The compact spaces exhibit an interesting behaviour with respect to known cardinal functions: the hereditary density of the powers Kk 2n is countable up to k = n and it is uncountable (even the spread is uncountable) for k > n. © Instytut Matematyczny PAN, 2011.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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