Constructions preserving n -weak amenability of Banach algebras

A. Jabbari; Mohammad Sal Moslehian; H. R. E. Vishki

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 4, page 349-357
  • ISSN: 0862-7959

Abstract

top
A surjective bounded homomorphism fails to preserve n -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

How to cite

top

Jabbari, A., Moslehian, Mohammad Sal, and Vishki, H. R. E.. "Constructions preserving $n$-weak amenability of Banach algebras." Mathematica Bohemica 134.4 (2009): 349-357. <http://eudml.org/doc/38097>.

@article{Jabbari2009,
abstract = {A surjective bounded homomorphism fails to preserve $n$-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.},
author = {Jabbari, A., Moslehian, Mohammad Sal, Vishki, H. R. E.},
journal = {Mathematica Bohemica},
keywords = {weak amenability; $n$-weak amenability; derivation; second dual; direct sum; Banach algebra; Arens product; weak amenability; -weak amenability; derivation; second dual; direct sum; Banach algebra; Arens product},
language = {eng},
number = {4},
pages = {349-357},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Constructions preserving $n$-weak amenability of Banach algebras},
url = {http://eudml.org/doc/38097},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Jabbari, A.
AU - Moslehian, Mohammad Sal
AU - Vishki, H. R. E.
TI - Constructions preserving $n$-weak amenability of Banach algebras
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 4
SP - 349
EP - 357
AB - A surjective bounded homomorphism fails to preserve $n$-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
LA - eng
KW - weak amenability; $n$-weak amenability; derivation; second dual; direct sum; Banach algebra; Arens product; weak amenability; -weak amenability; derivation; second dual; direct sum; Banach algebra; Arens product
UR - http://eudml.org/doc/38097
ER -

References

top
  1. Arens, A., 10.1090/S0002-9939-1951-0045941-1, Proc. Amer. Math. Soc. 2 (1951), 839-848. (1951) Zbl0044.32601MR0045941DOI10.1090/S0002-9939-1951-0045941-1
  2. Bade, W. G., Curtis, P. C., Dales, H. G., Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc. 55 (1987), 359-377. (1987) Zbl0634.46042MR0896225
  3. Dales, H. G., Banach Algebras and Automatic Continuity, London Math. Soc. Monographs Vol. 24, Clarendon Press, Oxford (2000). (2000) Zbl0981.46043MR1816726
  4. Dales, H. G., Ghahramani, F., Grønbæk, N., Derivations into iterated duals of Banach algebras, Studia Math. 128 (1998), 19-54. (1998) MR1489459
  5. Dales, H. G., Lau, A. T.-M., The second duals of Beurling algebras, Mem. Amer. Math. Soc. 177 (2005). (2005) Zbl1075.43003MR2155972
  6. Ghahramani, F., Laali, J., 10.1017/S0004972700020232, Bull. Austral. Math. Soc. 65 (2002), 191-197. (2002) Zbl1029.46116MR1898533DOI10.1017/S0004972700020232
  7. Gronbæk, N., 10.1017/S1446788700034649, J. Austral. Math. Soc. (Series A) 51 (1991), 483-488. (1991) MR1125449DOI10.1017/S1446788700034649
  8. Gronbæk, N., Weak and cyclic amenability for non-commutative Banach algebras, Proc. Edinburgh Math. Soc. 35 (1992), 315-328. (1992) MR1169250
  9. Helemskii, A. Ya., The Homology of Banach and Topological Algebras, Kluwer, Dordrecht (1989). (1989) MR1093462
  10. Hewitt, E., Ross, K. A., Abstract Harmonic Analysis, Vol. I, Springer, Berlin (1963); Vol. II, Springer, Berlin, 1970. Zbl0837.43002MR0551496
  11. Johnson, B. E., 10.1112/blms/23.3.281, Bull. London Math. Soc. 23 (1991), 281-284. (1991) Zbl0757.43002MR1123339DOI10.1112/blms/23.3.281
  12. Leptin, H., Sur l'algèbre de Fourier d'un groupe localement compact, C. R. Acad. Sci. Paris, Sér. A 266 (1968), 1180-1182. (1968) Zbl0169.46501MR0239002
  13. 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
  14. Runde, V., 10.1007/b82937, Lecture Notes in Mathematics Vol. 1774, Springer (2002). (2002) Zbl0999.46022MR1874893DOI10.1007/b82937
  15. Zhang, Y., 10.1090/S0002-9947-02-03039-8, Trans. Amer. Math. Soc. 354 (2002), 4131-4151. (2002) Zbl1008.46019MR1926868DOI10.1090/S0002-9947-02-03039-8

NotesEmbed ?

top

You must be logged in to post comments.