# Generalization of the weak amenability on various Banach algebras

Madjid Eshaghi Gordji; Ali Jabbari; Abasalt Bodaghi

Mathematica Bohemica (2019)

- Volume: 144, Issue: 1, page 1-11
- ISSN: 0862-7959

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topEshaghi Gordji, Madjid, Jabbari, Ali, and Bodaghi, Abasalt. "Generalization of the weak amenability on various Banach algebras." Mathematica Bohemica 144.1 (2019): 1-11. <http://eudml.org/doc/294721>.

@article{EshaghiGordji2019,

abstract = {The generalized notion of weak amenability, namely $(\varphi ,\psi )$-weak amenability, where $\varphi ,\psi $ are continuous homomorphisms on a Banach algebra $\{\mathcal \{A\}\}$, was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the $(\varphi ,\psi )$-weak amenability on the measure algebra $M(G)$, the group algebra $L^1(G)$ and the Segal algebra $S^1(G)$, where $G$ is a locally compact group, are studied. As a typical example, the $(\varphi ,\psi )$-weak amenability of a special semigroup algebra is shown as well.},

author = {Eshaghi Gordji, Madjid, Jabbari, Ali, Bodaghi, Abasalt},

journal = {Mathematica Bohemica},

keywords = {Banach algebra; $(\varphi ,\psi )$-derivation; group algebra; locally compact group; measure algebra; Segal algebra; weak amenability},

language = {eng},

number = {1},

pages = {1-11},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Generalization of the weak amenability on various Banach algebras},

url = {http://eudml.org/doc/294721},

volume = {144},

year = {2019},

}

TY - JOUR

AU - Eshaghi Gordji, Madjid

AU - Jabbari, Ali

AU - Bodaghi, Abasalt

TI - Generalization of the weak amenability on various Banach algebras

JO - Mathematica Bohemica

PY - 2019

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 144

IS - 1

SP - 1

EP - 11

AB - The generalized notion of weak amenability, namely $(\varphi ,\psi )$-weak amenability, where $\varphi ,\psi $ are continuous homomorphisms on a Banach algebra ${\mathcal {A}}$, was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the $(\varphi ,\psi )$-weak amenability on the measure algebra $M(G)$, the group algebra $L^1(G)$ and the Segal algebra $S^1(G)$, where $G$ is a locally compact group, are studied. As a typical example, the $(\varphi ,\psi )$-weak amenability of a special semigroup algebra is shown as well.

LA - eng

KW - Banach algebra; $(\varphi ,\psi )$-derivation; group algebra; locally compact group; measure algebra; Segal algebra; weak amenability

UR - http://eudml.org/doc/294721

ER -

## References

top- Bade, W. G., Jr., P. C. Curtis, Dales, H. G., 10.1093/plms/s3-55_2.359, Proc. Lond. Math. Soc., III. Ser. 55 (1987), 359-377. (1987) Zbl0634.46042MR0896225DOI10.1093/plms/s3-55_2.359
- Bodaghi, A., Module $(\varphi ,\psi )$-amenability of Banach algeras, Arch. Math., Brno 46 (2010), 227-235. (2010) Zbl1240.43001MR2754062
- Bodaghi, A., Generalized notion of weak module amenability, Hacet. J. Math. Stat. 43 (2014), 85-95. (2014) Zbl1327.46047MR3185637
- Bodaghi, A., Gordji, M. Eshaghi, Medghalchi, A. R., 10.15352/bjma/1240336430, Banach J. Math. Anal. 3 (2009), 131-142. (2009) Zbl1163.46034MR2461753DOI10.15352/bjma/1240336430
- Bodaghi, A., Shojaee, B., A generalized notion of $n$-weak amenability, Math. Bohemica 139 (2014), 99-112. (2014) Zbl1340.46040MR3231432
- Dales, H. G., Ghahramani, F., Helemskii, A. Ya., 10.1112/S0024610702003381, J. Lond. Math. Soc., II. Ser. 66 (2002), 213-226. (2002) Zbl1015.43002MR1911870DOI10.1112/S0024610702003381
- Dales, H. G., Pandey, S. S., 10.1090/S0002-9939-99-05139-4, Proc. Am. Math. Soc. 128 (2000), 1419-1425. (2000) Zbl0952.43003MR1641681DOI10.1090/S0002-9939-99-05139-4
- Despić, M., Ghahramani,, F., 10.4153/CMB-1994-024-4, Can. Math. Bull. 37 (1994), 165-167. (1994) Zbl0813.43001MR1275699DOI10.4153/CMB-1994-024-4
- Ghahramani, F., Lau, A. T. M., 10.1017/S0305004102005960, Math. Proc. Camb. Philos. Soc. 133 (2002), 357-371. (2002) Zbl1010.46048MR1912407DOI10.1017/S0305004102005960
- Grønbæk, N., 10.4064/sm-94-2-149-162, Studia Math. 94 (1989), 149-162. (1989) Zbl0704.46030MR1025743DOI10.4064/sm-94-2-149-162
- Hewitt, E., Ross, K. A., 10.1007/978-1-4419-8638-2, Grundlehren der mathematischen Wissenschaften 115. A Series of Comprehensive Studies in Mathematics. Springer, Berlin (1979). (1979) Zbl0416.43001MR0551496DOI10.1007/978-1-4419-8638-2
- Johnson, B. E., Cohomology in Banach Algebras, Mem. Am. Math. Soc. 127. AMS, Providence (1972). (1972) Zbl0256.18014MR0374934
- Johnson, B. E., 10.1112/blms/23.3.281, Bull. Lond. Math. Soc. 23 (1991), 281-284. (1991) Zbl0757.43002MR1123339DOI10.1112/blms/23.3.281
- 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
- Moslehian, M. S., Motlagh, A. N., Some notes on $(\sigma ,\tau )$-amenability of Banach algebras, Stud. Univ. Babeş-Bolyai, Math. 53 (2008), 57-68. (2008) Zbl1199.46111MR2487108
- Reiter, H., Stegeman, J. D., Classical Harmonic Analysis and Locally Compact Groups, London Mathematical Society Monographs. New Series 22. Clarendon Press, Oxford (2000). (2000) Zbl0965.43001MR1802924
- Zhang, Y., 10.4153/CMB-2001-050-7, Can. Math. Bull. 44 (2001), 504-508. (2001) Zbl1156.46306MR1863642DOI10.4153/CMB-2001-050-7

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