Operator Connes-amenability of completely bounded multiplier Banach algebras

Bahman Hayati; Abasalt Bodaghi; Massoud Amini

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 1, page 31-42
  • ISSN: 0044-8753

Abstract

top
For a completely contractive Banach algebra B , we find conditions under which the completely bounded multiplier algebra ℳ c b ( B ) is a dual Banach algebra and the operator amenability of B is equivalent to the operator Connes-amenability of ℳ c b ( B ) . We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.

How to cite

top

Hayati, Bahman, Bodaghi, Abasalt, and Amini, Massoud. "Operator Connes-amenability of completely bounded multiplier Banach algebras." Archivum Mathematicum 055.1 (2019): 31-42. <http://eudml.org/doc/294443>.

@article{Hayati2019,
abstract = {For a completely contractive Banach algebra $B$, we find conditions under which the completely bounded multiplier algebra $\mathcal \{M\}_\{cb\}(B)$ is a dual Banach algebra and the operator amenability of $B$ is equivalent to the operator Connes-amenability of $\mathcal \{M\}_\{cb\}(B)$. We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.},
author = {Hayati, Bahman, Bodaghi, Abasalt, Amini, Massoud},
journal = {Archivum Mathematicum},
keywords = {amenability; Connes-amenability; dual multiplier algebra; normal virtual operator diagonal},
language = {eng},
number = {1},
pages = {31-42},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Operator Connes-amenability of completely bounded multiplier Banach algebras},
url = {http://eudml.org/doc/294443},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Hayati, Bahman
AU - Bodaghi, Abasalt
AU - Amini, Massoud
TI - Operator Connes-amenability of completely bounded multiplier Banach algebras
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 1
SP - 31
EP - 42
AB - For a completely contractive Banach algebra $B$, we find conditions under which the completely bounded multiplier algebra $\mathcal {M}_{cb}(B)$ is a dual Banach algebra and the operator amenability of $B$ is equivalent to the operator Connes-amenability of $\mathcal {M}_{cb}(B)$. We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.
LA - eng
KW - amenability; Connes-amenability; dual multiplier algebra; normal virtual operator diagonal
UR - http://eudml.org/doc/294443
ER -

References

top
  1. Daws, M., 10.7146/math.scand.a-15010, Math. Scand. 99 (2006), 217–246. (2006) MR2289023DOI10.7146/math.scand.a-15010
  2. Daws, M., Multipliers, self-induced and dual Banach algebras, Dissertationes Math. (Rozprawy Mat.) 470 (2010), 62 pp. (2010) MR2681109
  3. Deutsch, E., 10.1007/BF02162408, Numer. Math. 19 (1) (1970), 73–84. (1970) MR0277552DOI10.1007/BF02162408
  4. Effros, E.G., Ruan, Z.-J., Operator Spaces, Clarendon Press, 2000. (2000) MR1793753
  5. Hayati, B., Amini, M., 10.1215/0023608X-2009-003, Kyoto J. Math. 50 (2010), 41–50. (2010) MR2629641DOI10.1215/0023608X-2009-003
  6. Hayati, B., Amini, M., 10.5486/PMD.2015.7043, Publ. Math. Debrecen 86 (2015), 169–182. (2015) MR3300584DOI10.5486/PMD.2015.7043
  7. Helmeskii, A.Ya., 10.1070/SM1991v068n02ABEH001374, Math. USSR.-Sb. 68 (1991), 555–566. (1991) DOI10.1070/SM1991v068n02ABEH001374
  8. Johnson, B.E., 10.1112/plms/s3-14.2.299, Proc. London Math. Soc. 14 (1964), 299–320. (1964) MR0159233DOI10.1112/plms/s3-14.2.299
  9. Johnson, B.E., Cohomology in Banach Algebras, Mem. Amer. Math. Soc. 127 (1972). (1972) Zbl0256.18014MR0374934
  10. Johnson, B.E., 10.1112/jlms/50.2.361, J. London Math. Soc. 50 (2) (1994), 361–374. (1994) MR1291743DOI10.1112/jlms/50.2.361
  11. Johnson, B.E., Kadison, R.V., Ringrose, J.R., 10.24033/bsmf.1731, Bull. Soc. Math. France 100 (1972), 73–96. (1972) MR0318908DOI10.24033/bsmf.1731
  12. Larsen, R., An Introduction to the Theory of Mutipliers, Springer-Verlag, Berlin, 1971. (1971) MR0435738
  13. Oshobi, E.O., Pym, J.S., 10.1017/S0305004100067542, Math. Proc. Cambridge Philos. Soc. 102 (1987), 481–505. (1987) MR0906623DOI10.1017/S0305004100067542
  14. Ruan, Z.-J., 10.2307/2375026, Amer. J. Math. 117 (1995), 1449–1474. (1995) MR1363075DOI10.2307/2375026
  15. Runde, V., 10.4064/sm148-1-5, Studia Math. 148 (2001), 47–66. (2001) Zbl1003.46028MR1881439DOI10.4064/sm148-1-5
  16. Runde, V., Lectures on Amenability, Lecture Notes in Math., vol. 1774, Springer-Verlag, Berlin-Heidelberg-New York, 2002. (2002) Zbl0999.46022MR1874893
  17. Runde, V., 10.1112/S0024610703004125, J. London Math. Soc. 67 (2003), 643–656. (2003) MR1967697DOI10.1112/S0024610703004125
  18. Runde, V., 10.1017/S0004972700037709, Bull. Austral. Math. Soc. 68 (2003), 325–328. (2003) MR2016307DOI10.1017/S0004972700037709
  19. Runde, V., 10.7146/math.scand.a-14452, Math. Scand. 95 (2004), 124–144. (2004) MR2091485DOI10.7146/math.scand.a-14452
  20. Runde, V., Spronk, N., 10.1017/S030500410300745X, Math. Proc. Cambridge Philos. Soc. 136 (2004), 675–686. (2004) MR2055055DOI10.1017/S030500410300745X
  21. Runde, V., Uygul, F., Connes-amenability of Fourier-Stieltjes algebras, Bull. London Math. Soc. (2015). (2015) MR3375923
  22. Spronk, N., Measurable Schur multiplies and completely bounded multipliers of the Fourier algebras, Proc. London Math. Soc. 89 (2004), 161–192. (2004) MR2063663

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.