L ∞ Spaces of Vector-Valued Functions as Spaces of Continuous Functions
It is proved that for any decomposable perfect measure space ( , , ), the space ∗∞ ( , *) of essentially bounded weak* measurable functions on to * is linearly isometric to the space ( , ∗*) of continuous functions on to ∗*, the latter space is being provided with the supremum norm ‖ ‖∞ = sup ∈ ‖ (...
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| Published in: | Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi Vol. 19; no. 1; pp. 1 - 7 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
27.05.2024
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| ISSN: | 1306-7575, 1306-7575 |
| Online Access: | Get full text |
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| Summary: | It is proved that for any decomposable perfect measure space ( , , ), the space ∗∞ ( , *) of essentially bounded weak* measurable functions on to * is linearly isometric to the space ( , ∗*) of continuous functions on to ∗*, the latter space is being provided with the supremum norm ‖ ‖∞ = sup ∈ ‖ ( )‖ where ∗* stands for the space * endowed with its weak* topology. |
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| ISSN: | 1306-7575 1306-7575 |
| DOI: | 10.29233/sdufeffd.1396580 |