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In this paper, it is proved that the predual bimodule of the measure algebra of an infinite discrete group is not injective despite the fact that the measure algebra of an amenable group is amenable in the sense of Connes. Thus the well-known result of Khelemskii (claiming that, for a von Neumann algebra, Connes-amenability is equivalent to the condition that the predual bimodule is injective) cannot be extended to measure algebras. Moreover, for a discrete amenable group, we give a simple formula for a normal virtual diagonal of the measure algebra. It is shown that a certain canonical bimodule over the measure algebra is not normal. 相似文献
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Seytek B. Tabaldyev 《Central European Journal of Mathematics》2014,12(3):470-475
Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to . 相似文献
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It is shown that if is an infinite, metrizable, compact spacesuch that some finite order iterated derived set of is empty,then dgC()=dbC()=2. 2000 Mathematics Subject Classification46M20 (primary), 46J10 (secondary). 相似文献
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S. B. Tabaldyev 《Functional Analysis and Its Applications》2006,40(3):244-246
Let Ω be a metrizable compact space. Suppose that its derived set of some finite order is empty. Let B be a unital Banach algebra, and let $\widehat \otimes $ stand for the projective tensor product. We prove the additivity formulas dg C(Ω)B $\widehat \otimes $ =dgB and db C(Ω) $\widehat \otimes $ B=dbC(Ω)+dbB for the global homological dimension and the homological bidimension. Thus these formulas are true for a new class of commutative Banach algebras in addition to those considered earlier by Selivanov. 相似文献
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S. B. Tabaldyev 《Mathematical Notes》2006,80(5-6):715-725
We prove that, for each nonnegative integer n and n = ∞, there exists a compact topological space Ω such that the strict global dimension and the strict bidimension of the Banach algebra C(Ω) of all continuous functions on Ω are equal to n. We also obtain several “additivity formulas” for the strict homological dimensions of strict Banach algebras. 相似文献
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S. B. Tabaldyev 《Moscow University Mathematics Bulletin》2014,69(4):164-168
It is proved that if A = C(Ω), where Ω is an infinite metrizable compact space such that some finite-order iterated derived set of Ω is empty, then for every unital Banach algebra B the global dimensions and the bidimensions of the Banach algebras A \(\hat \otimes \) B and B are related as dg A \(\hat \otimes \) B = 2 + dg B and db A \(\hat \otimes \) B = 2 + db B. Thus, a partial extension of Selivanov’s result is obtained. 相似文献
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