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
Main Author: Güntürk, Banu
Format: Journal Article
Language:English
Published: 27.05.2024
ISSN:1306-7575, 1306-7575
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Abstract 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.
AbstractList 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.
Author Güntürk, Banu
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Cites_doi 10.1090/S0002-9939-1982-0647896-5
10.1007/978-3-642-88047-6
10.2307/1968472
10.1007/978-1-4615-7819-2
10.1007/BF01214177
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10.1090/S0002-9947-1972-0295110-3
10.1007/BFb0068175
10.1090/surv/015
10.1007/978-3-642-65669-9
10.1090/S0002-9947-1938-1501970-8
10.1007/978-94-009-9260-3_6
10.1007/978-3-642-65970-6
10.1090/S0002-9939-1992-1027088-7
10.1007/978-3-642-65762-7
10.3906/mat-1705-119
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