# On pseudo-amenability of Beurling algebras

## TL;DR

This paper characterizes amenability and pseudo-amenability of Beurling algebras on specific semigroups and groups, providing equivalence conditions and extending the discussion to locally compact groups.

## Contribution

It offers new characterizations and conditions for amenability and pseudo-amenability of Beurling algebras on semigroups and groups, including equivalence criteria.

## Key findings

- Characterization of amenability and pseudo-amenability for specific semigroups.
- Equivalence conditions for amenability of Beurling algebras.
- Discussion of pseudo-amenability for locally compact groups.

## Abstract

Amenability and pseudo-amenability of $ \ell^{1}(S,\omega) $ is characterized, where $S$ is a left (right) zero semigroup or it is a rectangular band semigroup. The equivalence conditions to amenability of $\ell^{1}(S,\omega)$ are provided, where $ S $ is a band semigroup. For a locally compact group $G$, pseudo-amenability of $ \ell^{1}(G,\omega) $ is also discussed.