Some topological and geometric properties of generalized Euler sequence space

被引：28

作者：

Kara, Emrah Evren ^{[1
]}

Ozturk, Mahpeyker ^{[1
]}

Basarir, Metin ^{[1
]}

机构：

[1] Sakarya Univ, Dept Math, TR-54187 Sakarya, Turkey

来源：

MATHEMATICA SLOVACA | 2010年 / 60卷 / 03期

关键词：

Euler sequence space; paranormed sequence space; alpha-; beta-; gamma-duals; property (H); rotund property; LUR property; MATRIX TRANSFORMATIONS; INCLUDE; L(P);

D O I：

10.2478/s12175-010-0019-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce the Euler sequence space e (r) (p) of nonabsolute type and prove that the spaces e (r) (p) and l(p) are linearly isomorphic. Besides this, we compute the alpha-, beta- and gamma-duals of the space e (r) (p). The results proved herein are analogous to those in [ALTAY, B.-BASAR, F.: On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26 (2002), 701-715] for the Riesz sequence space r (q) (p). Finally, we define a modular on the Euler sequence space e (r) (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 e (r) (p) has property (H) but it is not rotund (R).

引用

页码：385 / 398

页数：14

共 16 条

[1] On the Euler sequence spaces which include the spaces lp and l∞I [J].