ACTA issues

## The Banach algebra $S_{\alpha }$ and applications

Bruno de Malafosse

Acta Sci. Math. (Szeged) 70:1-2(2004), 125-145
5804/2009

 Abstract. In this paper we put together some applications given in [7] and [8]. First we deal with the notion of a basis of $\alpha$, $\beta$ type and with the expansion of a function in a power series. Then we deal with the finite section method for operators mapping $s_{\alpha }$ into itself. AMS Subject Classification (1991): 46A15 Keyword(s): Infinite linear system, operator of first-difference, unital Banach algebra, BK space Received November 1, 2002, and in final form March 17, 2003. (Registered under 5804/2009.)