Compact operators on the Hahn space

On the New Generalized Hahn Sequence Space h d p

“…In this section, we first calculate the γ − dual of the space h d and then we give some basic lemmas to prove the α − , β − and γ − duals of the space h p d . The following calculations on the β − dual of the space h d has been stated by Goes ([11], 4.1 Theorem, p. 485) and it has recently been proved by Malkowsky et al [12], Proposition 2.3., p.5) as…”

“…Most recently, Malkowsky at al [12] defined the generalized Hahn sequence space h d , where d is an unbounded monotone increasing sequence of positive real numbers, and characterized several classes of bounded linear operators or matrix transformations from…”

“…Quiet recently a scientific study of a more generalized Hahn sequence space h d , is carried out by Malkowsky et al [12], defined as follows:…”

Modeling Spheres in Some Paranormed Sequence Spaces

“…and ∆x k = x k − x k+1 for all k. In the special cases, where d k = k or d k = 1 for all k, the generalized Hahn space reduces to the original Hahn space h or the classical space bv 0 (see, for instance [14], Definition 7.3.3), respectively. It was shown in [15], Proposition 2.1, that if the sequence d is increasing and unbounded, then h d is a BK space with AK. Matrix transformations and bounded and compact operators on the Hahn space have recently been studied in various papers, for instance in [5,[15][16][17][18][19][20][21][22][23].…”

“…It was shown in [15], Proposition 2.1, that if the sequence d is increasing and unbounded, then h d is a BK space with AK. Matrix transformations and bounded and compact operators on the Hahn space have recently been studied in various papers, for instance in [5,[15][16][17][18][19][20][21][22][23]. Spectra on the Hahn space were studied in [16,24,25].…”