Introducing Statistical Operators: Boundedness, Continuity, and Compactness
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929384453046272 |
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| author | Bayram, Erdal Küçükaslan, Mehmet Et, Mikail Aydın, Abdullah |
| author_facet | Bayram, Erdal Küçükaslan, Mehmet Et, Mikail Aydın, Abdullah |
| contents | Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research related to operator theory. As far as we know, no studies have focused on continuous, bounded, and compact operators, which are fundamental concepts in mathematics. We explore the notions of statistical boundedness, continuity, and compactness of operators between normed spaces, establishing connections between these concepts and their counterparts in traditional normed space theory. Additionally, we provide examples and results that demonstrate the behavior and implications of statistical convergence in the context of operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Introducing Statistical Operators: Boundedness, Continuity, and Compactness Bayram, Erdal Küçükaslan, Mehmet Et, Mikail Aydın, Abdullah Functional Analysis Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research related to operator theory. As far as we know, no studies have focused on continuous, bounded, and compact operators, which are fundamental concepts in mathematics. We explore the notions of statistical boundedness, continuity, and compactness of operators between normed spaces, establishing connections between these concepts and their counterparts in traditional normed space theory. Additionally, we provide examples and results that demonstrate the behavior and implications of statistical convergence in the context of operators. |
| title | Introducing Statistical Operators: Boundedness, Continuity, and Compactness |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.08560 |