Abstract
In this paper, we investigate the notion of approximate biprojectivity for semigroup algebras and for some Banach algebras related to semigroup algebras. We show that $$\ell ^{1}(S)$$ is approximately biprojective if and only if $$\ell ^{1}(S)$$ is biprojective, provided that $$S$$ is a uniformly locally finite inverse semigroup. Also for a Clifford semigroup $$S$$ , we show that approximate biprojectivity of $$\ell ^{1}(S)^{**}$$ gives pseudo-amenability of $$\ell ^{1}(S)$$ . We give a class of Banach algebras related to semigroup algebras which is not approximately biprojective.
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