On the Euler sequence spaces which include the spaces l(p) and l(infinity)I

Altay B., Basar F., Mursaleen M.

INFORMATION SCIENCES, cilt.176, ss.1450-1462, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 176 Konu: 10
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.ins.2005.05.008
  • Sayfa Sayıları: ss.1450-1462


In the present paper, we introduce the Euler sequence space e(p)(r) consisting of all sequences whose Euler transforms of order r are in the space e,, of non-absolute type which is the BK-space including the space l(p) and prove that the spaces e(p)(r) and l(p) are linearly isomorphic for 1 <= p <= infinity. Furthermore, we give some inclusion relations concerning the space e(p)(r). Finally, we determine the alpha-, beta- and gamma-duals of the space e(p)(r) for 1 <= p <= infinity and construct the basis for the space e(p)(r), where 1 <= P <= infinity. (c) 2005 Elsevier Inc. All rights reserved.