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

Yıl 2018, Cilt: 67 Sayı: 1, 235 - 241, 01.02.2018

Mahmut Işık

https://doi.org/10.1501/Commua1_0000000845

Cited By: 2

Öz

Let `1 and c denote the Banach spaces of real bounded and convergent sequences
x = (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
(n) =


k1
(n)

; k = 1; 2; ::: .A continuous linear functional ' on `1 is said
to be an invariant mean or a mean if and only if
(i) ' (x) 0 when xn 0 for all n;
(ii) ' (e) = 1; where e = (1; 1; 1; :::) and
(iii) '
x(n)
= ' (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

Anahtar Kelimeler

Modulus function, sequence spaces, seminorm

Kaynakça

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• Current address : Harran University, Faculty of Education, Sanliurfa-TURKEY E-mail address : [e-mail]