International Journal of Functional Analysis, Operator Theory and Applications
Volume 2, Issue 1, Pages 85 - 95
(June 2010)
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ANOTHER PROOF OF THE BISHOP-MACHADO THEOREM
B. Brosowski and A. R. Da Silva
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Abstract:
In this paper, we give an alternative proof of the well-known Bishop-Machado theorem (see, e.g., [5], [8] and [11]). By using techniques introduced in [4], we substitute approximate partitions of unity, usually employed for this purpose, by a corresponding construction in the Dedekind-MacNeille completion of certain subsets of continuous functions. |
| Keywords and phrases: Bishop-Machado theorem, Dedekind-MacNeille completion. |
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