Some New Paranormed Sequence Spaces and $\alpha-$ Core

Serkan Demiriz; Celal Çakan

Some New Paranormed Sequence Spaces and $\alpha-$ Core

Functional Analysis 2014-12-03 v1

Authors: Serkan Demiriz , Celal Çakan

Abstract

In this study, we define new paranormed sequence spaces by combining a double sequential band matrix and a diagonal matrix. Furthermore, we compute the $\alpha-,\beta-$ and $\gamma-$ duals and obtain bases for these sequence spaces. Besides this, we characterize the matrix transformations from the new paranormed sequence spaces to the spaces $c_{0}(q),c(q),\ell(q)$ and $\ell_{\infty}(q)$ . Finally, $\alpha-core$ of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.

Cite

@article{arxiv.1412.0891,
  title  = {Some New Paranormed Sequence Spaces and $\alpha-$ Core},
  author = {Serkan Demiriz and Celal Çakan},
  journal= {arXiv preprint arXiv:1412.0891},
  year   = {2014}
}

Comments

16 pages. arXiv admin note: substantial text overlap with arXiv:1309.0154; and text overlap with arXiv:1105.3747 by other authors

Some New Paranormed Sequence Spaces and $\alpha-$ Core

Abstract

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