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Some topological and geometric properties of generalized Euler sequence space

In: Mathematica Slovaca, vol. 60, no. 3
Emrah Evren Kara - Mahpeyker Őztürk - Metin Başarir
Detaily:
Rok, strany: 2010, 385 - 398
Kľúčové slová:
Euler sequence space, paranormed sequence space, $\alpha$-, $\beta$-, $\gamma$-duals, property (H), rotund property, LUR property
O článku:
In this paper, we introduce the Euler sequence space $er(p)$ of non-absolute type and prove that the spaces $er(p)$ and $l(p)$ are linearly isomorphic. Besides this, we compute the $α$-, $β$- and $γ$-duals of the space $er(p)$. The results proved herein are analogous to those in [ALTAY, B.—BAŞAR, F.: \textit{On the paranormed Riesz sequence spaces of non-absolute type}, Southeast Asian Bull. Math. \textbf{26} (2002), 701–715] for the Riesz sequence space $rq(p)$. Finally, we define a modular on the Euler sequence space $er(p)$ and consider it equipped with the Luxemburg norm. We give some relationships between the modular and Luxemburg norm on this space and show that the space $er(p)$ has property (H) but it is not rotund $(R)$.
Ako citovať:
ISO 690:
Kara, E., Őztürk, M., Başarir, M. 2010. Some topological and geometric properties of generalized Euler sequence space. In Mathematica Slovaca, vol. 60, no.3, pp. 385-398. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0019-5

APA:
Kara, E., Őztürk, M., Başarir, M. (2010). Some topological and geometric properties of generalized Euler sequence space. Mathematica Slovaca, 60(3), 385-398. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0019-5
O vydaní: