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.)
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