Some Topological and Geometrical Properties of a New Difference Sequence Space
We introduce the new difference sequence space 𝑎𝑟𝑝(Δ) . Further, it is proved that the space 𝑎𝑟𝑝(Δ) is the BK-space including the space 𝑏𝑣𝑝, which is the space of sequences of pbounded variation. We also show that the spaces 𝑎𝑟𝑝(Δ), and ℓ𝑝 are linearly isomorphic for 1≤𝑝<∞. Furthermore, the b...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/213878 |
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| Summary: | We introduce the new difference sequence space 𝑎𝑟𝑝(Δ) . Further, it is
proved that the space 𝑎𝑟𝑝(Δ) is the BK-space including the space 𝑏𝑣𝑝, which is the space of sequences of pbounded
variation. We also show that the spaces 𝑎𝑟𝑝(Δ), and ℓ𝑝 are linearly isomorphic for 1≤𝑝<∞.
Furthermore, the basis and the 𝛼-, 𝛽- and
𝛾-duals of the space 𝑎𝑟𝑝(Δ) are determined. We devote
the final section of the paper to examine some geometric properties of the space 𝑎𝑟𝑝(Δ). |
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| ISSN: | 1085-3375 1687-0409 |