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Disposition of points on a sphere of a Banach space and modulus of continuity of a function

โœ Scribed by V. A. Yudin


Publisher
SP MAIK Nauka/Interperiodica
Year
1984
Tongue
English
Weight
387 KB
Volume
35
Category
Article
ISSN
0001-4346

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๐Ÿ“œ SIMILAR VOLUMES


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โœ M. Allame; B. Vatankhahan ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 175 KB

Let f (x) be a periodic function with period T . In Rivlin (1969) [1] it is claimed that the modulus of continuity is independent of a on [a, a + T ]. In this note we show that this is not correct.

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Let C(X) be the Banach space of continuous real-valued functions of an infinite compacturn X with the sup-norm, which is homeomorphic to the pseudo-interior s = (-I, I)"' of the Hilbert cube Q = [-1, llw. We can regard C(X) as a subspace of the hyperspace exp(X x E) of nonempty compact subsets of X