On some new paranormed euler sequence spaces and Euler Core


DEMİRİZ S., Cakan C.

ACTA MATHEMATICA SINICA-ENGLISH SERIES, cilt.26, ss.1207-1222, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 26 Konu: 7
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1007/s10114-010-8334-x
  • Dergi Adı: ACTA MATHEMATICA SINICA-ENGLISH SERIES
  • Sayfa Sayıları: ss.1207-1222

Özet

In this paper, the sequence spaces e (0) (r) (u, p) and e (c) (r) (u, p) of non-absolute type which are the generalization of the Maddox sequence spaces have been introduced and it is proved that the spaces e (0) (r) (u, p) and e (c) (r) (u, p) are linearly isomorphic to spaces c (0)(p) and c(p), respectively. Furthermore, the alpha-, beta- and gamma-duals of the spaces e (0) (r) (u, p) and e (c) (r) (u, p) have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the class of matrices (e (0) (r) (u, p): A mu) has been characterized, where A mu is one of the sequence spaces a"" (a), c and c (0) and derives the other characterizations for the special cases of A mu. In the last section, Euler Core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.