Electronic Resource
Springer
Annali di matematica pura ed applicata
117 (1978), S. 233-242
ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary If X is a Hilbert space and V is a subspace, given x ε X/V the best approximation IIv(x) to x from V can be constructed in the following way: we consider a ball Br centered at x and intersecting V, then we take the (Chebyshev) center of Br ∩ V. In Banach spaces the centers in V of Br ∩ V (which depend on r) are related to a different map of « approximation ». Here we introduce the notions of « sheltered point » and « shelter » of a bounded set, and we obtain in Banach spaces information about IIv(x) starting from the shelter of Br ∩ V. The notion of sheltered point turns out to be of some interest by itself, since translates problems of simultaneous worst approximation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02417893
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