On the space of bounded Euler difference sequences and some classes of compact operators

A note on compact operators on matrix domains

“…In this final section, we will some results on compact operators studied in [7] and [8], but in a different way applying our general results. Many of them are the same, but some of them are the corrected and improved versions of the previous ones.…”

“…In [7] and [8] the author studied the sequence spaces a r c ( ), a r 0 ( ) and a r ∞ ( ) (0 < r < 1), considering them as matrix domains of a triangle T in c, c 0 and ∞ , namely a r c ( ) = (c) T , a r 0 ( ) = (c 0 ) T and a r ∞ ( ) = ( ∞ ) T , where T = (t nk ) ∞ n,k=0 is given by…”

“…These results are applied to characterise some special classes of compact operators on the spaces studied in [7,8].…”

On B(m)${B^{(m)}}$-difference sequence spaces using generalized means and compact operators

“…If = + 1, = 1 + , where 0 < < 1, = 1 for all and = 1, = −1, = 1, then the sequence spaces ( , , ; ( ) ) for ∈ { , 0 } reduce to the spaces (Δ) and 0 (Δ), respectively, studied by Aydin and Başar [4]. For = ∞ , the sequence space ( , , ; ( ) ) reduces to ∞ (Δ) studied by Djolović [11]. V. If = ( ) is a strictly increasing sequence of positive real numbers tending to in nity such that = , = − −1 , = 1 and = 1, = −1, = 1, then the spaces ( , , ; ( ) ) for ∈ { , 0 } reduce to 0 (Δ) and (Δ), respectively, studied by Mursaleen and Noman [23].…”

“…This can be achieved with the help of Hausdor measure of noncompactness. Recently several authors, among them Malkowsky and Rakočević [17], Djolović [11], Mursaleen and Noman [21,22,25], Başarir and Kara [5][6][7], Mohiuddine et al [20], have established some identities or estimates for the operator norms and the Hausdor measure of noncompactness of matrix operators from an arbitrary space to an arbitrary space. Let us recall some de nitions and well-known results.…”