Başar Feyzi, Karaisa Ali
Department of Mathematics, Faculty of Arts and Sciences, Fatih University, Hadımköy Campus, Büyükçekmece, 34500 İstanbul, Turkey.
Department of Mathematics & Computer Science, Faculty of Science, Necmettin Erbakan University, Meram Campus, Meram, 42090 Konya, Turkey.
ScientificWorldJournal. 2013 Nov 14;2013:349346. doi: 10.1155/2013/349346. eCollection 2013.
We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1≤p≤∞, respectively, and prove that ℓpλ(B) and ℓ p are linearly isomorphic for 0<p≤∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we construct the basis for the space ℓpλ(B), where 1≤p<∞. Furthermore, we determine the alpha-, beta- and gamma-duals of the space ℓpλ(B) for 1≤p≤∞. Finally, we investigate some geometric properties concerning Banach-Saks type p and give Gurarii's modulus of convexity for the normed space ℓpλ(B).
我们引入非绝对型序列空间ℓpλ(B)，在0<p<1和1≤p≤∞的情况下，它分别是一个p赋范空间和BK空间，并证明对于0<p≤∞，ℓpλ(B)和ℓ p是线性同构的。此外，我们给出了一些关于空间ℓpλ(B)的包含关系，并构造了1≤p<∞时空间ℓpλ(B)的基。此外，我们确定了1≤p≤∞时空间ℓpλ(B)的α-、β-和γ-对偶。最后，我们研究了关于巴拿赫-萨克斯型p的一些几何性质，并给出了赋范空间ℓpλ(B)的古拉瑞凸性模。
