A generalized notion of $n$-weak amenability

@article{Bodaghi2014,
abstract = {In the current work, a new notion of $n$-weak amenability of Banach algebras using homomorphisms, namely $(\varphi ,\psi )$-$n$-weak amenability is introduced. Among many other things, some relations between $(\varphi ,\psi )$-$n$-weak amenability of a Banach algebra $\mathcal \{A\}$ and $M_\{m\}(\mathcal \{A\})$, the Banach algebra of $m\times m$ matrices with entries from $\mathcal \{A\}$, are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra $L^1(G)$ is ($\varphi ,\psi $)-$n$-weakly amenable for any bounded homomorphisms $\varphi $ and $\psi $ on $L^1(G)$.},
author = {Bodaghi, Abasalt, Shojaee, Behrouz},
journal = {Mathematica Bohemica},
keywords = {Banach algebra; continuous homomorphism; $(\varphi ,\psi )$-derivation; $n$-weak amenability; Banach algebra; continuous homomorphism; $(\varphi ,\psi )$-derivation; -weak amenability},
language = {eng},
number = {1},
pages = {99-112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A generalized notion of $n$-weak amenability},
url = {http://eudml.org/doc/261077},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Bodaghi, Abasalt
AU - Shojaee, Behrouz
TI - A generalized notion of $n$-weak amenability
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 1
SP - 99
EP - 112
AB - In the current work, a new notion of $n$-weak amenability of Banach algebras using homomorphisms, namely $(\varphi ,\psi )$-$n$-weak amenability is introduced. Among many other things, some relations between $(\varphi ,\psi )$-$n$-weak amenability of a Banach algebra $\mathcal {A}$ and $M_{m}(\mathcal {A})$, the Banach algebra of $m\times m$ matrices with entries from $\mathcal {A}$, are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra $L^1(G)$ is ($\varphi ,\psi $)-$n$-weakly amenable for any bounded homomorphisms $\varphi $ and $\psi $ on $L^1(G)$.
LA - eng
KW - Banach algebra; continuous homomorphism; $(\varphi ,\psi )$-derivation; $n$-weak amenability; Banach algebra; continuous homomorphism; $(\varphi ,\psi )$-derivation; -weak amenability
UR - http://eudml.org/doc/261077
ER -