Weakly Connes amenable dual Banach algebras
We shall develop a notion of amenability for dual Banach algebras, namely weak Connes amenability, which will play the role that weak amenability does for usual Banach algebras
math.FA↗
arXiv subjects
Amin Mahmoodi
Publications and source records attributed to Amin Mahmoodi.
Pointwise amenable, non-amenable Banach algebras
It is shown that a pointwise amenable Banach algebra need not be amenable. This positively answer a question raised by Dales, Ghahramani and Loy.
math.FA↗
On pseudo-amenability of Beurling algebras
Amenability and pseudo-amenability of $ \ell^{1}(S,ω) $ is characterized, where $S$ is a left (right) zero semigroup or it is a rectangular band semigroup. The equivalence conditions to amenability of $\ell^{1}(S,ω)$ are provided, where $ S $ is a band semigroup. For a locally compact group $G$, pseudo-amenability of $ \ell^{1}(G,ω) $ is also discussed.
math.FA↗
Pointwise amenability for dual Banach algebras
We shall develop two notions of pointwise amenability, namely pointwise Connes amenability and pointwise $w^*$-approximate Connes amenability, for dual Banach algebras which take the $w^*$-topology into account. We shall study these concepts for the Banach sequence algebras $\ell^1(ω)$ and the weighted semigroup algebras $ \ell^{1}(\mathbb{N}_{\wedge},ω)$. For a weight $ω$ on a discrete semigroup $S$, we shall investigate pointwise amenability/Connes amenability of $\ell^1(S,ω)$ in terms of diagonals.
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$φ$-contractibility and $φ$-Connes amenability coincide with some older notions
It is shown that various definitions of $φ$-Connes amenability as introduced independently in \cite{Gh-Ja, mah, Sh-Am}, are just rediscovering existing notions and presenting them in different ways. It is also proved that even $φ$-contractibility as defined in \cite{Sangani}, is equivalent to an older and simpler concept.
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Biflat-like Banach algebras
Given a Banach algebra $ \mathcal{A} $ and a continuous homomorphism $σ$ on it, the notion of $σ$-biflatness for $ \mathcal{A} $ is introduced. This is a generalization of biflatness and it is shown that they are distinct. The relations between $σ$-biflatness and some other close concepts such as $σ$-biprojectivity and $σ$-amenability are studied. The $σ$-biflatness of tensor product of Banach algebras are also discussed.
math.FA↗