Strong algebrability of C^* algebras

Theory of Approximation and Applications

مقاله 1، دوره 15، شماره 2، اسفند 2021، صفحه 1-13   

نوع مقاله: Research Articles

نویسنده

Alireza Soleimani^*

Faculty of Mathematics, Tarbiat Modares University, tehran, iran

چکیده

In this paper, we introduce the concept strong algebrability of certain C^* algebras generated by finite generators. In fact, using Gelfand theorem, we identify the members of the C^* algebra generated by one element, with the continuous functions on its spectrum, and use some recent result for strong algebrability for functions spaces.
Moreover, we introduce the new concept unitable elements in unital C^* algebras, and then we express our main result for this kind of elements. In fact, the C^* subalgebra generated by a non unitable element in a C^* algebra is strongly c algebrable.
As the last result in this paper, we show 2^c strong algebrability of direct sums of C^* algebras, using non unitable elements of them

کلیدواژه‌ها

C^* algebras؛ algebrability؛ lineability