Paper's Title:

To a Banach *-algebra in a Semipartial Dynamical System

Author(s):

Bahman Tabatabaie Shourijeh and Seyed Mostafa Zebarjad

Department of Mathematics,
College of Sciences,
Shiraz University, Shiraz 71454,
Iran.

E-mail: tabataba@math.susc.ac.ir    
zebarjad@mail.yu.ac.ir
URL: http://research.shirazu.ac.ir/faculty/More.asp?ID=207

Abstract:

By a partial dynamical system, we mean a triple containing a C*-algebra A, a discrete group G and a partial action of G on A. There are two C*--algebras associated to a given partial dynamical system. These are nothing but the certain C*-completions of a Banach *-algebra. In constructing such a Banach *-algebra, usually, a tedious limit process is used to apply. In this paper, we prove some theorems in this context without any limit process.

Paper's Title:

Partial Semigroup Algebras Associated to Partial Action

Author(s):

Bahman Tabatabaie Shourijeh and Sahar Moayeri Rahni

Department of Mathematics,
College of Sciences, Shiraz University,
Shiraz, 71454,
Iran.
E-mail: tabataba@math.susc.ac.ir

Department of Mathematics,
College of Sciences, Shiraz University,
Shiraz, 71454,
Iran.
E-mail: smoayeri@shirazu.ac.ir

Abstract:

For a given inverse semigroup S, we introduce the notion of algebraic crossed product by using a given partial action of S, and we will prove that under some condition it is associative. Also we will introduce the concept of partial semigroup algebra K_Par(S), and we show that the suitable quotient of K_Par(S) is a kind of crossed product.