On some new paranormed euler sequence spaces and Euler Core |
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| Authors: | Serkan Demiriz Celal Çakan |
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| Institution: | (1) NASA Goddard Space Flight Center, 587, Greenbelt, MD 20771, USA;(2) NASA Goddard Space Flight Center (GSFC), Greenland, MD 20771, USA;(3) Lockheed Martin, Advanced Technology Laboratories, Arlington, VA, USA;(4) Viable Systems, Inc., 4710 Bethesda Ave. #516, Maryland, MD 20814, USA;(5) NASA Goddard Space Flight Center, 585, Greenbelt, MD 20771, USA;(6) Lero-the Irish Software Engineering Research Centre, University of Limerick, Limerick, Ireland;(7) Computer Science Research Institute, University of Ulster, Newtownabbey, County Antrim, Northern Ireland |
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| Abstract: | 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 α-, β- and γ-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): μ) has been characterized, where μ is one of the sequence spaces ℓ
∞, c and c
0 and derives the other characterizations for the special cases of μ. 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. |
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| Keywords: | sequence spaces matrix transformations core of a sequence |
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