On left ϕ -biflat Banach algebras

Amir Sahami; Mehdi Rostami; Abdolrasoul Pourabbas

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 3, page 337-344
  • ISSN: 0010-2628

Abstract

top
We study the notion of left ϕ -biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra S ( G ) is left ϕ -biflat if and only if G is amenable. Also we characterize left ϕ -biflatness of semigroup algebra l 1 ( S ) in terms of biflatness, when S is a Clifford semigroup.

How to cite

top

Sahami, Amir, Rostami, Mehdi, and Pourabbas, Abdolrasoul. "On left $\varphi $-biflat Banach algebras." Commentationes Mathematicae Universitatis Carolinae 61.3 (2020): 337-344. <http://eudml.org/doc/297031>.

@article{Sahami2020,
abstract = {We study the notion of left $\varphi $-biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra $S(G)$ is left $\varphi $-biflat if and only if $G$ is amenable. Also we characterize left $\varphi $-biflatness of semigroup algebra $l^\{1\}(S)$ in terms of biflatness, when $S$ is a Clifford semigroup.},
author = {Sahami, Amir, Rostami, Mehdi, Pourabbas, Abdolrasoul},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {left $\varphi $-biflat; Segal algebra; semigroup algebra; locally compact group},
language = {eng},
number = {3},
pages = {337-344},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On left $\varphi $-biflat Banach algebras},
url = {http://eudml.org/doc/297031},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Sahami, Amir
AU - Rostami, Mehdi
AU - Pourabbas, Abdolrasoul
TI - On left $\varphi $-biflat Banach algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 3
SP - 337
EP - 344
AB - We study the notion of left $\varphi $-biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra $S(G)$ is left $\varphi $-biflat if and only if $G$ is amenable. Also we characterize left $\varphi $-biflatness of semigroup algebra $l^{1}(S)$ in terms of biflatness, when $S$ is a Clifford semigroup.
LA - eng
KW - left $\varphi $-biflat; Segal algebra; semigroup algebra; locally compact group
UR - http://eudml.org/doc/297031
ER -

References

top
  1. Alaghmandan M., Nasr-Isfahani R., Nemati M., 10.1017/S0004972710000286, Bull. Aust. Math. Soc. 82 (2010), no. 2, 274–281. MR2685151DOI10.1017/S0004972710000286
  2. Essmaili M., Rostami M., Amini M., 10.3336/gm.51.1.04, Glas. Mat. Ser. III 51(71) (2016), no. 1, 45–58. MR3516184DOI10.3336/gm.51.1.04
  3. Ghahramani F., Lau A. T. M., 10.1017/S0305004102005960, Math. Proc. Cambridge Philos. Soc. 133 (2002), no. 2, 357–371. MR1912407DOI10.1017/S0305004102005960
  4. Ghahramani F., Loy R. J., Willis G. A., 10.1090/S0002-9939-96-03177-2, Proc. Amer. Math. Soc. 124 (1996), no. 5, 1489–1497. MR1307520DOI10.1090/S0002-9939-96-03177-2
  5. Hewitt E., Ross K. A., Abstract Harmonic Analysis I: Structure of Topological Groups. Integration Theory, Group Representations, Die Grundlehren der mathematischen Wissenschaften, 115, Academic Press, Springer, Berlin, 1963. MR0156915
  6. Howie J. M., Fundamental of Semigroup Theory, London Mathematical Society Monographs, New Series, 12, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995. MR1455373
  7. Hu Z., Monfared M. S., Traynor T., 10.4064/sm193-1-3, Studia Math. 193 (2009), no. 1, 53–78. MR2506414DOI10.4064/sm193-1-3
  8. Javanshiri H., Nemati M., 10.36045/bbms/1547780429, Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 5, 687–698. MR3901840DOI10.36045/bbms/1547780429
  9. Kaniuth E., Lau A. T., Pym J., 10.1017/S0305004107000874, Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 1, 85–96. MR2388235DOI10.1017/S0305004107000874
  10. Ramsden P., 10.1007/s00233-009-9169-6, Semigroup Forum 79 (2009), no. 3, 515–530. MR2564061DOI10.1007/s00233-009-9169-6
  11. Reiter H., L 1 -algebras and Segal Algebras, Lecture Notes in Mathematics, 231, Springer, Berlin, 1971. MR0440280
  12. Runde V., Lectures on Amenability, Lecture Notes in Mathematics, 1774, Springer, Berlin, 2002. MR1874893

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.