Nonisomorphy of certain Banach spaces of smooth functions to the space of continuous functions
โ Scribed by N. G. Sidorenko
- Publisher
- Springer US
- Year
- 1988
- Tongue
- English
- Weight
- 226 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0016-2663
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๐ SIMILAR VOLUMES
We show among other things that if B is a Banach function space of continuous real-valued functions vanishing at infinity on a locally compact Hausdorff space X, with the property that for some odd natural number p>1, b 1ร p # B for all b # B, then B=C 0 (X ).
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
It is shown that if a separable real Banach space X admits a separating analytic ลฝ ลฝ . function with an additional condition property K , concerning uniform behaviour . of radii of convergence then every uniformly continuous mapping on X into any real Banach space Y can be approximated by analytic o