Davoud FOROUTANNIA

On the block sequence space $l_p(E)$ and related matrix transformations

The purpose of the present study is to introduce the sequence space $$l_p(E)=\left\{ x=(x_n)_{n=1}^{\infty}\;:\; \sum_{n=1}^{\infty} \left|\sum_{j\in E_n}x_j\right|^p

Anahtar Kelimeler:

Sequence spaces, matrix domains, $\alpha$- and $\beta$-duals, matrix transformations

On the block sequence space $l_p(E)$ and related matrix transformations

The purpose of the present study is to introduce the sequence space $$l_p(E)=\left\{ x=(x_n)_{n=1}^{\infty}\;:\; \sum_{n=1}^{\infty} \left|\sum_{j\in E_n}x_j\right|^p

Keywords:

Sequence spaces, matrix domains, $\alpha$- and $\beta$-duals, matrix transformations,

PDF

___

Altay B, Ba¸sar F. Some Euler sequence spaces of non-absolute type. Ukr Math J 2005; 57: 1–17.
Altay B, Ba¸sar F. Some paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull Math 2006; : 591–608.
Altay B, Ba¸sar F. The fine spectrum and the matrix domain of the diﬀerence operator ∆ on the sequence space lp, (0 < p < 1) . Commun Math Anal 2007; 2: 1–11.
Altay B, Ba¸sar F, Malkowsky E. Matrix transformations on some sequence spaces related to strong Ces`aro summa- bility and boundedness. Appl Math Comput 2009; 211: 255–264.
Altay B, Ba¸sar F, Mursaleen M. On the Euler sequence spaces which include the spaces lpand l∞. Inform Sci ; 176: 1450–1462.
Ba¸sar F. Summability Theory and Its Applications. ˙Istanbul, Turkey: Bentham Science Publishers, 2012.
Ba¸sar F, Altay B. On the space of sequences of p-bounded variation and related matrix mappings. Ukr Math J ; 55: 136–147. Ba¸sar F, Altay B, Mursaleen M. Some generalizations of the space bvp of p-bounded variation sequences. Nonlinear Anal 2008; 68: 273–287.
Erfanmanesh S, Foroutannia D. Some new semi-normed sequence spaces of non-absolute type and matrix transfor- mations TWMS J Pure Appl Math (in press). Malkowsky E, Rakoˇcevi´c V. An introduction into the theory of sequence spaces and measures of noncompactness. Zbornik Radova Matematiˇcki Institut SANU Belgrade 2000; 9: 143–243.
Mursaleen M, Ba¸sar F, Altay B. On the Euler sequence spaces which include the spaces lpand l∞II. Nonlinear Anal 2006; 65: 707–717.
Mursaleen M, Noman AK. On some new diﬀerence sequence spaces of non-absolute type. Math Comput Modelling ; 52: 603–617. Ng PN, Lee PY. Ces`aro sequence spaces of non-absolute type. Comment Math Prace Mat 1978; 20: 429–433.
S¸eng¨on¨ul M, Ba¸sar F. Some new Ces`aro sequence spaces of non-absolute type which include the spaces c0and c . Soochow J Math 2005; 31: 107–119.
Wang CS. On N¨orlund sequence spaces. Tamkang J Math 1978; 9: 269–274.
Ye¸silkayagil M, Ba¸sar F. On the paranormed N¨orlund sequence space of non-absolute type. Abstr Appl Anal 2014; : 858704.