ON THE ACTION OF A LINEAR OPERATOR OVER SEQUENCES IN A BANACH-SPACE

In this paper we study the action of a bounded linear operator over di fferent kinds of sequences of a Banach space. Our work is mainly devot ed to minimal and M-basic sequences. PLANS and GARCIA CASTELLON have c haracterized the boundedness of a linear operator T by requiring the m inimality of any sequence whose image is a minimal sequence (e. g. [P, 1969], [GC, 1990]). We extend these results to other types of sequenc es like M-basic, basic, strong M-basic, etc.. We are also interested o n conditions that ensure the minimality of the image of a given minima l sequence. Thus in Corollary 3.7 we characterize semi-Fredholm operat ors as those which transform every p-minimal sequence into q-minimal. In the last section we deal with M-basis whose image is M-basis or nor ming M-basis or basis or in general the ''best'' possible sequence.