Warianty tytułu
Języki publikacji
Abstrakty
In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with Ј-weak amenability and ideal amenability, where Ј is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/Ј-weak amenability and of Ј-weak amenabilitydo not coincide for Banach algebras in general.
Czasopismo
Rocznik
Tom
Strony
20--28
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran, teymuri.math@gmail.com
autor
- Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran, abasalt.bodaghi@gmail.com
autor
- Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran, e_bagha@yahoo.com
Bibliografia
- [1] Johnson B. E., Cohomology in Banach algebras, Mem. Amer. Math. Soc., 1972, 127
- [2] Bade W. G., Curtis P. G., Dales H. G., Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc., 1987, 55(3), 359–377
- [3] Gorgi M. E., Yazdanpanah T., Derivations into duals of ideals of Banach algebras, Proc. Indian Acad. Sci. (Math. Sci.), 2004, 114(4), 399–408
- [4] Minapoor A., Bodaghi A., Ebrahimi Bagha D., Ideal Connes-amenability of dual Banach algebras, Mediterr. J. Math., 2017, 14:174. https://doi.org/10.1007/s00009-017-0970-2
- [5] Haagerup U., Laustsen N. J., Weak amenability of C*-algebras and a theorem of Goldstein, In: Albrecht E., Mathieu M. (Eds.), Banach algebras ’97, Walter de Gruyter, Berlin, 1998, 223-244
- [6] Haagerup U., All nuclear C*-algebras are amenable, Invent. Math., 1983, 74, 30–319
- [7] Runde V., Lectures on Amenability, Lecture Notes in Math., vol. 1774, Springer-Verlag Berlin Heidelberg, 2002
- [8] Johnson B. E., White M. C., A non-weakly amenable augmentation ideal, preprint
- [9] Dales H. G., Banach algebra and automatic continuity, Clarendon press, Oxford, 2000
- [10] Gordji M. E., Hayati B., Hosseinioun S. A. R., Ideal amenability of Banach algebras and some hereditary properties, J. Sci., Islamic Rep. Iran., 2010, 21(4), 333–341
- [11] Roe J., Notes on operator algebras, Fall 2000, http://www.personal.psu.edu/jxr57/520/notes.pdf
- [12] Connes A., On the cohomology of operator algebras, J. Funct. Anal., 1978, 28, 243–253
- [13] Wassermann S., On tensor products of certain group C*-algebras, J. Funct. Anal., 1976, 23, 28–36
- [14] Dales H. G., Lau A. T.-M., Strauss D., Banach algebras on semigroups and on their compactifications, Mem. Amer. Math. Soc., 2010, 205(966)
- [15] Ghahramani F., Loy R. J., Willis G. A., Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc., 1996, 124, 1489–1497
- [16] Forrest B., Kaniuth E., Lau A. T.-M., Spronk N., Ideals with bounded approximate identities in Fourier algebras, J. Funct. Math. Anal., 2003, 203, 286–304
- [17] Johnson B. E., Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc., 1994, 50(2), 361–374
- [18] Grønbæk N., Weak and cyclic amenable for non-commutative Banach algebra, Proc. Edinburg Math. Soc., 1992, 35, 315–328
- [19] Grønbæk N., Weak amenability of group algebras, Bull. London Math. Soc., 1991, 23, 231–284
- [20] Defant A., Floret K., Tensor norms and operator ideals, vol. 176, North-Holland Mathematics studies, 1992
- [21] Mewomo O. T., On ideal amenability in Banach algebras, Ann. Alex. Ioan Cuza Uni.-Mathematics, 2010, Tomul LVI, 273–278
- [22] Jabbari A., On ideal ameability of Banach algebras, J. Math. Phy. Anal. Geom., 2012, 8(2), 135–143
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-397d2697-2f7a-48c6-b784-a062f1ba12f1