L ∞ Spaces of Vector-Valued Functions as Spaces of Continuous Functions

Authors : Banu Güntürk

Pages : 1-7

Doi:10.29233/sdufeffd.1396580

View : 50 | Download : 27

Publication Date : 2024-05-27

Article Type : Research Paper

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.
Keywords : ∞ Space, Vector Valued Functions, Perfect Measure, Hyperstonean Space, Continuous Function Spaces