Related papers: A note on left $\phi$-biflat Banach algebras

In this paper, we introduce a homological notion of left $\phi$-biprojectivity for Banach algebras, where $\phi$ is a non-zero multiplicative linear functional. We show that for a locally compact group $G$, the Segal algebra $S(G)$ is left…

In this paper, we study left $\phi$-biflatness and left $\phi$-biprojectivity of some Banach algebras, where $\phi$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $\phi$-biprojective, then…

In this paper we are going to investigate the approximate biprojectivity and the $\phi$-biflatness of some Banach algebras related to the locally compact groups. We show that a Segal algebra $S(G)$ is approximate biprojective if and only if…

In this paper, for a Banach algebra A, we introduced the new notions of approximately left $\phi$-biprojective and approximately left character biprojective, where $\phi$ is a non-zero multiplicative linear functional on A. We show that for…

In this paper, we study the notion of approximately bi at Banach algebras for second dual Banach algebras and semigroup algebras. We show that for a locally compact group G, if S(G)?? is approximately bi at, then G is amenable group. Also…

In this paper, we study the notion of $\phi$-biflatness, $\phi$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples…

Given a Banach algebra $ \mathcal{A} $ and a continuous homomorphism $\sigma$ on it, the notion of $\sigma$-biflatness for $ \mathcal{A} $ is introduced. This is a generalization of biflatness and it is shown that they are distinct. The…

In this paper, we countinue our work in \cite{11}. We show that $L^{1}(G,w)$ is $\phi_{0}$-biprojective if and only if $G$ is compact, where $\phi_{0}$ is the augmentation character. We introduce the notions of character Johnson amenability…

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L1(G), and the Fourier algebra, A(G), of a locally compact group, G.

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 $\ell^{1}(S)$…

In this paper we define module biprojctivity and module biflatness for a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find their relation to classical biprojectivity and biflatness. As a…

Building on an old result of Duncan and Namioka, we show that the ${\ell}^1$-convolution algebra of a semilattice $S$ is biflat precisely when $S$ is uniformly locally finite. The proof shows in passing that for such $S$ the convolution…

In this paper we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some Matrix algebras. Using this tool, we characterize strong pseudo-amenability of $\ell^{1}(S)$, provided that…

In this note, we prove that a semigroup $S$ is left amenable if and only if every two nonzero elements of $\ell^1_+(S)$ have a common nonzero right multiple, where $\ell^1_+(S)$ is the positive part of the Banach algebra $\ell^1(S)$, or…

Let $\mathfrak{A}$ be a Banach algebra, and $\mathcal{X}$ a Banach $\mathfrak{A}$-bimodule. A bounded linear mapping $\mathcal{D}:\mathfrak{A}\rightarrow \mathcal{X}$ is approximately semi-inner derivation if there eixist nets…

Let $S$ be an inverse semigroup with the set of idempotents $E$. In this paper we define the module super-amenability of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and show that when $E$…

In this paper, we study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X,$ the Lipschitz algebras $Lip_{\alpha}(X)$ and $\ell…

Let $G$ be a locally compact group and $(\Phi, \Psi)$ be a complementary pair of $N$-functions. In this paper, using the powerful tool of porosity, it is proved that when $G$ is an amenable group, then the Fig\`a-Talamanca-Herz-Orlicz…

Certain semigroups are known to admit a `strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the $\ell^1$-convolution algebras of such semigroups, and obtain a disintegration…

We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity.…