Uniform bounds for point cohomology of $\ell^1(\mathbb Z_+)$ and related algebras

Choi, Yemon (2009) Uniform bounds for point cohomology of $\ell^1(\mathbb Z_+)$ and related algebras. Journal of Mathematical Analysis and Applications, 358 (2). pp. 249-260. ISSN 0022-247X

Abstract

The point cohomology of the convolution algebra ℓ1(Z+) is known to vanish 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 ℓ1(Z+). Analogous results are obtained for some other L1-algebras which arise from ‘rank one’ subsemigroups of R+.