Abstract

In this paper Z, R, and C denote the sets of integer, real and complex numbers, respectively. I stands for the unit circle in C. Given complex Banach spaces X, Y. L (X, Y) stands for the space of all bounded linear operators from X to Y. For a linear operator A on X we denote by o (A), p (A) its spectrum and resolvent set. The space of all bounded sequences (r (n)), z CX is denoted by l,(X). For a natural number r we denote the Banach space C:=(p:(-r,-r+ 1,---, 0)–X) with norn||:= sup,...,-| p (n)|| If r; Z–X, r, e C stands for the function r,(6)= r (n+ 6), Yn GZ,–r< 3< 0