SOME PROPERTIES OF SEQUENCE SPACE _ BV (f p q s)

Authors : Mahmut IŞIK

Pages : 235-241

Doi:10.1501/Commua1_0000000845

View : 16 | Download : 9

Publication Date : 2018-02-01

Article Type : Research Paper

Abstract :Let `1 and c denote the Banach spaces of real bounded and convergent sequences x = insert ignore into journalissuearticles values(xn); normed by kxk = sup n jxnj ; respectively. Let be a one to one mapping of the set of positive integers into itself such that k insert ignore into journalissuearticles values(n); = k1 insert ignore into journalissuearticles values(n); ; k = 1; 2; ::: .A continuous linear functional ` on `1 is said to be an invariant mean or a mean if and only if insert ignore into journalissuearticles values(i); ` insert ignore into journalissuearticles values(x); 0 when xn 0 for all n; insert ignore into journalissuearticles values(ii); ` insert ignore into journalissuearticles values(e); = 1; where e = insert ignore into journalissuearticles values(1; 1; 1; :::); and insert ignore into journalissuearticles values(iii); ` xinsert ignore into journalissuearticles values(n); = ` insert ignore into journalissuearticles values(fxng); for all x 2 `1: If is the translation mapping n ! n + 1; a mean is often called a Banach limit [3], and V is the set of convergent sequences, that is, the set of bounded sequences all of whose invariant means are equal, is the set ^f of almost convergent sequences
Keywords : Modulus function, sequence spaces, seminorm