On the dimension of left invariant means and left thick subsets

Topologically left invariant means on semigroup algebras

Let M(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup S with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for M(S)∗ to have a topologically left invariant mean.

Uniform Convergence to a Left Invariance on Weakly Compact Subsets

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

Topologically Left Invariant Mean on Dual Semigroup Algebras

On Left Invariant

There is a well known one–parameter family of left invariant CR structures on SU(2) ∼= S. We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.

On the left and right cohomological dimension

In this paper we construct, for any 1 m; n 1, a nitely presented monoid with left cohomological dimension m and right cohomological dimension n.