Uniform bounds for point cohomology of $\ell^1({\mathbb Z}_+)$ and related algebras

Details Uniform bounds for point cohomology of $\ell^1({\mathbb Z}_+)$ and related algebras Uniform bounds for point cohomology of $\ell^1({\mathbb Z}_+)$ and related algebras

2008-08-16

arxiv.org/abs/0808.2265v4

J. Math. Anal. Appl. 358 (2009), no. 2, 249--260

Mathematics

Functional Analysis

19 pages, submitted. Uses diagrams.sty macros. v2: 16 pp. same mathematical content, with some reorganization and trimming of

Scientific paper

10.1016/j.jmaa.2009.05.002

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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