Euler-Ces`aro difference spaces of bounded, convergent and null sequences
2016 ◽
Vol 47
(4)
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pp. 405-420
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In this paper, we introduce the spaces $\breve{\ell}_{\infty}$, $\breve{c}$ and $\breve{c}_{0}$ of Euler-Ces`aro bounded, convergent and null difference sequences and prove that the inclusions $\ell_{\infty}\subset\breve{\ell}_{\infty}$, $c\subset\breve{c}$ and $c_{0}\subset\breve{c}_{0}$ strictly hold. We show that the spaces $\breve{c}_{0}$ and $\breve{c}$ turn out to be the separable BK spaces such that $\breve{c}$ does not possess any of the following: AK property and monotonicity. We determine the alpha-, beta- and gamma-duals of the new spaces and characterize the matrix classes $(\breve{c}:\ell_{\infty})$, $(\breve{c}:c)$ and $(\breve{c}:c_0)$.
2020 ◽
Vol 44
(1-4)
◽
pp. 299-309
2018 ◽
Vol 36
(1)
◽
pp. 37
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2018 ◽
Vol 123
(1)
◽
pp. 51-71
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