| Title:
|
Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras (English) |
| Author:
|
Sahami, Amir |
| Author:
|
Omidi, Mohammad R. |
| Author:
|
Ghaderi, Eghbal |
| Author:
|
Zangeneh, Hamzeh |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
83-92 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X$, the Lipschitz algebras ${\rm Lip}_{\alpha}(X)$ and ${\rm lip}_{\alpha}(X)$ are approximately biflat if and only if $X$ is finite, provided that $0<\alpha<1$. We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat. (English) |
| Keyword:
|
approximate biflatness |
| Keyword:
|
Johnson pseudo-contractibility |
| Keyword:
|
Lipschitz algebra |
| Keyword:
|
triangular Banach algebra |
| MSC:
|
46H05 |
| MSC:
|
46H20 |
| MSC:
|
46M10 |
| idZBL:
|
Zbl 07217160 |
| idMR:
|
MR4093431 |
| DOI:
|
10.14712/1213-7243.2020.004 |
| . |
| Date available:
|
2020-04-30T11:19:47Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148077 |
| . |
| Reference:
|
[1] Askari-Sayah M., Pourabbas A., Sahami A.: Johnson pseudo-contractibility of certain Banach algebras and their nilpotent ideals.Anal. Math. 45 (2019), no. 3, 461–473. MR 3995373, 10.1007/s10476-019-0840-1 |
| Reference:
|
[2] Bade W. G., Curtis P. C. Jr., Dales H. G.: Amenability and weak amenability for Beurling and Lipschitz algebras.Proc. London Math. Soc. (3) 55 (1987), no. 2, 359–377. MR 0896225 |
| Reference:
|
[3] Biyabani E., Rejali A.: Approximate and character amenability of vector-valued Lipschitz algebras.Bull. Korean Math. Soc. 55 (2018), no. 4, 1109–1124. MR 3845950 |
| Reference:
|
[4] Dales H. G.: Banach Algebras and Automatic Continuity.London Mathematical Society Monographs, New Series, 24, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 2000. MR 1816726 |
| Reference:
|
[5] Dashti M., Nasr-Isfahani R., Soltani Renani S.: Character amenability of Lipschitz algebras.Canad. Math. Bull. 57 (2014), no. 1, 37–41. MR 3150714, 10.4153/CMB-2012-015-3 |
| Reference:
|
[6] Ghahramani F., Zhang Y.: Pseudo-amenable and pseudo-contractible Banach algebras.Math. Proc. Camb. Philos. Soc. 142 (2007), 111–123. Zbl 1118.46046, MR 2296395, 10.1017/S0305004106009649 |
| Reference:
|
[7] Gourdeau F.: Amenability of Banach algebras.Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 351–355. MR 0974991, 10.1017/S0305004100067840 |
| Reference:
|
[8] Gourdeau F.: Amenability of Lipschitz algebras.Math. Proc. Cambridge Philos. Soc. 112 (1992), no. 3, 581–588. MR 1178007, 10.1017/S0305004100071267 |
| Reference:
|
[9] Hu Z., Monfared M. S., Traynor T.: On character amenable Banach algebras.Studia Math. 193 (2009), no. 1, 53–78. MR 2506414, 10.4064/sm193-1-3 |
| Reference:
|
[10] Kaniuth E., Lau A. T., Pym J.: On $\phi$-amenability of Banach algebras.Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 1, 85–96. MR 2388235, 10.1017/S0305004107000874 |
| Reference:
|
[11] Kelley J. L.: General Topology.D. Van Nostrand Company, Toronto, 1955. Zbl 0518.54001, MR 0070144 |
| Reference:
|
[12] Runde V.: Lectures on Amenability.Lecture Notes in Mathematics, 1774, Springer, Berlin, 2002. MR 1874893 |
| Reference:
|
[13] Sahami A., Pourabbas A.: Johnson pseudo-contractibility of certain semigroup algebras.Semigroup Forum 97 (2018), no. 2, 203–213. MR 3852768, 10.1007/s00233-017-9912-3 |
| Reference:
|
[14] Sahami A., Pourabbas A.: Johnson pseudo-contractibility of various classes of Banach algebras.Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 2, 171–182. MR 3819120, 10.36045/bbms/1530065007 |
| Reference:
|
[15] Samei E., Spronk N., Stokke R.: Biflatness and pseudo-amenability of Segal algebras.Canad. J. Math. 62 (2010), no. 4, 845–869. MR 2674704, 10.4153/CJM-2010-044-4 |
| Reference:
|
[16] Weaver N.: Lipschitz Algebras.World Scientific Publishing Co., River Edge, 1999. MR 1832645 |
| . |
