A new 2-inner product on the space of p-summable sequences
In this paper, we wish to define a 2-inner product, non-standard, possibly with weights, on ℓp. For this purpose, we aim to obtain a different 2-norm ‖., .‖2,v,w, which is not equivalent to the usual 2-norm ‖., .‖p on ℓp (except with the condition p=2), satisfying the parallelogram law. We discuss t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X15000462 |
| Summary: | In this paper, we wish to define a 2-inner product, non-standard, possibly with weights, on ℓp. For this purpose, we aim to obtain a different 2-norm ‖., .‖2,v,w, which is not equivalent to the usual 2-norm ‖., .‖p on ℓp (except with the condition p=2), satisfying the parallelogram law. We discuss the properties of the induced 2-norm ‖., .‖2,v,w and its relationships with the usual 2-norm on ℓp. We also find that the 2-inner product ⟨., .|.⟩v,w is actually defined on a larger space. |
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| ISSN: | 1110-256X |