Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞
We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1⩽p⩽∞, respectively, and prove that ℓpλ(B) and ℓp are linearly isomorphic for 0<p⩽∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we co...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/349346 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1⩽p⩽∞, respectively, and prove that ℓpλ(B) and ℓp are linearly isomorphic for 0<p⩽∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we construct the basis for the space ℓpλ(B), where 1⩽p<∞. Furthermore, we determine the alpha-, beta- and gamma-duals of the space ℓpλ(B) for 1⩽p⩽∞. Finally, we investigate some geometric properties concerning Banach-Saks type p and give Gurarii's modulus of convexity for the normed space ℓpλ(B). |
|---|---|
| ISSN: | 1537-744X |