A generalized notion of n -weak amenability

Abasalt Bodaghi; Behrouz Shojaee

Mathematica Bohemica (2014)

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

Abstract

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In the current work, a new notion of n -weak amenability of Banach algebras using homomorphisms, namely ( ϕ , ψ ) - n -weak amenability is introduced. Among many other things, some relations between ( ϕ , ψ ) - n -weak amenability of a Banach algebra 𝒜 and M m ( 𝒜 ) , the Banach algebra of m × m matrices with entries from 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 ( ϕ , ψ )- n -weakly amenable for any bounded homomorphisms ϕ and ψ on L 1 ( G ) .

How to cite

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Bodaghi, 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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  9. Lau, A. T.-M., Loy, R. J., 10.1006/jfan.1996.3002, J. Funct. Anal. 145 (1997), 175-204. (1997) Zbl0890.46036MR1442165DOI10.1006/jfan.1996.3002
  10. Losert, V., The derivation problem for group algebras, Ann. Math. (2) 168 (2008), 221-246. (2008) Zbl1171.43004MR2415402
  11. Mewomo, O. T., Akinbo, G., A generalization of the n -weak amenability of Banach algebras, An. Ştiinţ. Univ. ``Ovidius'' Constanţa, Ser. Mat. 19 (2011), 211-222. (2011) Zbl1224.46095MR2785698
  12. Moslehian, M. S., Motlagh, A. N., Some notes on ( σ , τ ) -amenability of Banach algebras, Stud. Univ. Babes-Bolyai Math. 53 (2008), 57-68. (2008) Zbl1199.46111MR2487108
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