Mohammad Hassan FAROUGHI, Ghorban KHALILZADEH

The compact metric space of the lattice of varieties and $ast$- varieties of $C^{ast}$ -algebras

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Variety of Banach algebras is a non-empty class of Banach algebras in which there exist a family of laws such that all of its members satisfy all of the laws. In this paper, we have used merelym athematical items such as Banach algebras and varieties including Banach algebras in order to change the space of all varieties of Banach algebras into a compact metric space. We prove some theorems in the metric space of zero at infinityv arieties, define the $ast$-varieties of $ast$-algebra and prove many theorems about $ast$-varieties of$C^{ast}$-algebras.

PDF

___

[1] Bonsall, F. F. Duncan, J.: Complete Normed Algebras, Springer, 1973.
[2] Dixon, J.: C∗-algebras, North-Holland, Amesterdam, 1982.
[3] Dixon, P. G.: Characterizatin of closed subalgebras of B(H), Proc. Edinburgh Math. Soc.(2) 20 No. 3, 215-217 (1976/77).
[4] Dixon, P. G.: Variety of Banach algebras, Quart. J. Math. Oxford ser, (2) 27, 481-487 (1976).
[5] Faroughi, M. H.: Subsemivarieties of Q-algebras, Proc. Amer. Math. Soc. 129(4), 1005-1014 (2001).
[6] Faroughi, M. H.: Uncountable chains and antichains of varities of Banach algebras, J. Math. Analysis and Appl, 168(1), 184 -194 (1992).
[7] Murphy, J.: Gerard C∗-algebras and Operator Theory, Academic Press, Inc, Boston, 1990.