A NOTE ON S-ACTS AND BOUNDED LINEAR OPERATORS

Abstract

In this work, the properties of the certain operator have been studied by looking at the associated S-act of this operator, and conversely.  Some operators, for example such operator, one to one, onto operators have been looked.  On the other hand, basic mathematical interpretation understanding of S-acts, such as faithful, finitely generated, singular, separated, torsion free and noetherian acts.  We have found out the properties may be associated with S-act which has any of these properties.  Let V be a inner product space over a field F, T be a bounded operator on V , and let S = {e^x+y|x, y are independent variables in R} be the semigroup. Define θ : S × V \(\longrightarrow\) V by θ(e^x+y, v) = e\(^{T+T^{*}}\) (v). This function makes V a left S-act, denote by V\(_{T+T^{*}}\) and we call it the associated S-act of T + T^∗.