Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916119223205888 |
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| author | Moreno-Pulido, Soledad Barbieri, Giuseppina León-Saavedra, Fernando Pérez-Fernández, Francisco Javier Sala-Pérez, Antonio |
| author_facet | Moreno-Pulido, Soledad Barbieri, Giuseppina León-Saavedra, Fernando Pérez-Fernández, Francisco Javier Sala-Pérez, Antonio |
| contents | In this manuscript we characterize the completeness of a normed space through the strong lacunary (N-theta) and lacunary statistical convergence (S-theta) of series. A new characterization of weakly unconditionally Cauchy series through N-theta and S-theta is obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesaro convergence summability space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities Moreno-Pulido, Soledad Barbieri, Giuseppina León-Saavedra, Fernando Pérez-Fernández, Francisco Javier Sala-Pérez, Antonio Functional Analysis In this manuscript we characterize the completeness of a normed space through the strong lacunary (N-theta) and lacunary statistical convergence (S-theta) of series. A new characterization of weakly unconditionally Cauchy series through N-theta and S-theta is obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesaro convergence summability space. |
| title | Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2402.06369 |