Home σ-symmetric amenability of Banach algebras
Article
Licensed
Unlicensed Requires Authentication

σ-symmetric amenability of Banach algebras

  • Lin Chen EMAIL logo , Mohammad Javad Mehdipour and Jun Li
Published/Copyright: March 26, 2024
Become an author with De Gruyter Brill

Abstract

In this paper, we introduce the notion of σ-symmetric amenability of Banach algebras and investigate some hereditary properties of them. We also apply our results to several abstract Segal algebras and group algebras.

Award Identifier / Grant number: 12061018

Funding statement: This work is supported by the National Natural Science Foundation of China (No. 12061018).

Acknowledgements

The authors wish to thank anonymous reviewers for their constructive and valuable suggestions which have considerably improved the presentation of the paper.

References

[1] M. Alaghmandan, R. Nasr-Isfahani and M. Nemati, Character amenability and contractibility of abstract Segal algebras, Bull. Aust. Math. Soc. 82 (2010), no. 2, 274–281. 10.1017/S0004972710000286Search in Google Scholar

[2] J. Alaminos, M. Mathieu and A. R. Villena, Symmetric amenability and Lie derivations, Math. Proc. Cambridge Philos. Soc. 137 (2004), no. 2, 433–439. 10.1017/S0305004104007637Search in Google Scholar

[3] A. Bodaghi, Module ( ϕ , ψ ) -amenability of Banach algebras, Arch. Math. (Brno) 46 (2010), no. 4, 227–235. Search in Google Scholar

[4] H. G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monogr. (N. S.) 24, Oxford University, New York, 2000. 10.1093/oso/9780198500131.001.0001Search in Google Scholar

[5] F. Ghahramani and A. T. M. Lau, Weak amenability of certain classes of Banach algebras without bounded approximate identities, Math. Proc. Cambridge Philos. Soc. 133 (2002), no. 2, 357–371. 10.1017/S0305004102005960Search in Google Scholar

[6] M. Ghasemi and M. J. Mehdipour, Homological properties of Banach modules related to locally compact groups, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 21 (2020), no. 4, 295–301. Search in Google Scholar

[7] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis. Vol. II: Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups, Grundlehren Math. Wiss. 152, Springer, New York, 1970. 10.1007/978-3-662-26755-4_3Search in Google Scholar

[8] H. İnceboz, B. Arslan and A. Bodaghi, Module symmetrically amenable Banach algebras, Acta Math. Acad. Paedagog. Nyházi. (N. S.) 33 (2017), no. 2, 233–245. Search in Google Scholar

[9] A. Jabbari and A. Ebadian, Characterization of symmetric amenability of unital Banach algebras, preprint (2020), https://arxiv.org/abs/2006.03823. Search in Google Scholar

[10] B. E. Johnson, Symmetric amenability and the nonexistence of Lie and Jordan derivations, Math. Proc. Cambridge Philos. Soc. 120 (1996), no. 3, 455–473. 10.1017/S0305004100075010Search in Google Scholar

[11] A. T. M. Lau and J. Pym, Concerning the second dual of the group algebra of a locally compact group, J. Lond. Math. Soc. (2) 41 (1990), no. 3, 445–460. 10.1112/jlms/s2-41.3.445Search in Google Scholar

[12] D. Malekzadeh Varnosfaderani, Derivations, multipliers and topological centers of certain banach algebras related to locally compact groups, Ph.D. Thesis, University of Manitoba, 2017. Search in Google Scholar

[13] M. J. Mehdipour and G. R. Moghimi, The existence of nonzero compact right multipliers and Arens regularity of weighted Banach algebras, Rocky Mountain J. Math. 52 (2022), no. 6, 2101–2112. 10.1216/rmj.2022.52.2101Search in Google Scholar

[14] M. J. Mehdipour and R. Nasr-Isfahani, Compact left multipliers on Banach algebras related to locally compact groups, Bull. Aust. Math. Soc. 79 (2009), no. 2, 227–238. 10.1017/S0004972708001147Search in Google Scholar

[15] M. J. Mehdipour and A. Rejali, Regularity and amenability of weighted Banach algebras and their second dual on locally compact groups, preprint (2021), https://arxiv.org/abs/2112.13286. Search in Google Scholar

[16] M. S. Monfared, Character amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 3, 697–706. 10.1017/S0305004108001126Search in Google Scholar

[17] M. S. Moslehian and A. N. Motlagh, Some notes on ( σ , τ ) -amenability of Banach algebras, Stud. Univ. Babeş-Bolyai Math. 53 (2008), no. 3, 57–68. Search in Google Scholar

Received: 2023-09-12
Revised: 2023-11-17
Accepted: 2023-11-30
Published Online: 2024-03-26
Published in Print: 2024-12-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 18.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/gmj-2024-2011/html
Scroll to top button