Exploration of indispensable Banach-space valued functions
In the paper, we present a necessary and sufficient condition for the existence of a sequence of measurable functions with finite values, which converge to any given essential bounded function in the topology of essential supremum in a Banach space. A new convergence method is proposed, which allows...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231416?viewType=HTML |
| Summary: | In the paper, we present a necessary and sufficient condition for the existence of a sequence of measurable functions with finite values, which converge to any given essential bounded function in the topology of essential supremum in a Banach space. A new convergence method is proposed, which allows for the discovery of an essential bounded function $ F $ that is valued in a Banach space. Generally speaking, there exists a Banach-valued essential bounded function $ F $ which $ F_n $ can't converge to $ F $ in the topology of essential supremum for any sequence of finite-valued measurable function. |
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| ISSN: | 2473-6988 |