$\ell^1({\mathbb Z}_+)$及相关代数的点上同调的一致界
Uniform bounds for point cohomology of $\ell^1({\mathbb Z}_+)$ and related algebras
摘要：
众所周知，卷积代数$\ell^1({\mathbb Z}_+)$的点上同调在2次及以上为零。我们锐化这一结果得到分裂映射的范数有界独立的点模的选择。我们的构造是$\ell^1({\mathbb Z}_+)$中极大理想的射影常数的新估计的副产品。对于由${\mathbb R}_+$的秩1子半群所产生的其它一些$L^1$ -代数，也得到了类似的结果.
英文摘要：
It is well-known that the point cohomology of the convolution algebra $\ell^1({\mathbb Z}_+)$ vanishes in degrees 2 and above. We sharpen this result by obtaining splitting maps whose norms are bounded independently of the choice of point module. Our construction is a by-product of new estimates on projectivity constants of maximal ideals in $\ell^1({\mathbb Z}_+)$. Analogous results are obtained for some other $L^1$-algebras which arise from `rank one' subsemigroups of ${\mathbb R}_+$.
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