# A generalized notion of $n$-weak amenability

Abasalt Bodaghi; Behrouz Shojaee

Mathematica Bohemica (2014)

- Volume: 139, Issue: 1, page 99-112
- ISSN: 0862-7959

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topBodaghi, Abasalt, and Shojaee, Behrouz. "A generalized notion of $n$-weak amenability." Mathematica Bohemica 139.1 (2014): 99-112. <http://eudml.org/doc/261077>.

@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 -

## References

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