Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summability
This study focuses on the development of novel vector-valued sequence spaces whose elements are characterized by constructing (weakly) multiplier $ \sigma $-convergent series. To achieve this, the concept of invariant means is rigorously examined and utilized as a foundational tool. These newly defi...
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025233 |
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| author | Mahmut Karakuş |
| author_facet | Mahmut Karakuş |
| author_sort | Mahmut Karakuş |
| collection | DOAJ |
| description | This study focuses on the development of novel vector-valued sequence spaces whose elements are characterized by constructing (weakly) multiplier $ \sigma $-convergent series. To achieve this, the concept of invariant means is rigorously examined and utilized as a foundational tool. These newly defined spaces are proven to possess the structure of Banach spaces when equipped with their natural sup norm, thus ensuring their completeness. In addition to establishing the Banach space properties, this study delves into the inclusion relationships between these new sequence spaces and classical multiplier spaces, specifically $ BMC(B) $ and $ CMC(B) $, where $ B $ denotes an arbitrary Banach space. By employing the $ \sigma $-convergence method, this study also culminates in a result analogous to the celebrated Hahn-Schur theorem, which traditionally establishes a connection between the weak convergence and the uniform convergence of unconditionally convergent series. |
| format | Article |
| id | doaj-art-e731e1a29d634d608c21f5a591e598e5 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e731e1a29d634d608c21f5a591e598e52025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-03-011035095510910.3934/math.2025233Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summabilityMahmut Karakuş0Department of Mathematics, Van Yüzüncü Yıl University, Van 65100, TurkeyThis study focuses on the development of novel vector-valued sequence spaces whose elements are characterized by constructing (weakly) multiplier $ \sigma $-convergent series. To achieve this, the concept of invariant means is rigorously examined and utilized as a foundational tool. These newly defined spaces are proven to possess the structure of Banach spaces when equipped with their natural sup norm, thus ensuring their completeness. In addition to establishing the Banach space properties, this study delves into the inclusion relationships between these new sequence spaces and classical multiplier spaces, specifically $ BMC(B) $ and $ CMC(B) $, where $ B $ denotes an arbitrary Banach space. By employing the $ \sigma $-convergence method, this study also culminates in a result analogous to the celebrated Hahn-Schur theorem, which traditionally establishes a connection between the weak convergence and the uniform convergence of unconditionally convergent series.https://www.aimspress.com/article/doi/10.3934/math.2025233multiplier convergencecompletenessuniform convergence$ \sigma $-convergencesummability methods |
| spellingShingle | Mahmut Karakuş Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summability AIMS Mathematics multiplier convergence completeness uniform convergence $ \sigma $-convergence summability methods |
| title | Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summability |
| title_full | Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summability |
| title_fullStr | Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summability |
| title_full_unstemmed | Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summability |
| title_short | Spaces of multiplier $ \sigma $-convergent vector valued sequences and uniform $ \sigma $-summability |
| title_sort | spaces of multiplier sigma convergent vector valued sequences and uniform sigma summability |
| topic | multiplier convergence completeness uniform convergence $ \sigma $-convergence summability methods |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025233 |
| work_keys_str_mv | AT mahmutkarakus spacesofmultipliersigmaconvergentvectorvaluedsequencesanduniformsigmasummability |