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Best simultaneous approximation in L-1 (mu, X)

Mendoza Casas, José and Pakhrou, Tijani (2007) Best simultaneous approximation in L-1 (mu, X). Journal of Approximation Theory, 145 (2). pp. 212-220. ISSN 0021-9045

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Let X be a Banach space, (Omega, Sigma, mu) a finite measure space, and L-1 (mu, X) the Banach space of X-valued Bochner mu-integrable functions defined on Omega endowed with its usual norm. Let us suppose that Sigma(0) is a sub-sigma-algebra of Sigma, and let mu(0) be the restriction of mu to Sigma(0). Given a natural number n, let N be a monotonous norm in R-n. It is shown that if X is reflexive then L-1 (mu(0), X) is N-simultaneously proximinal in L-1 (mu, X) in the sense of Fathi et al. [Best simultaneous approximation in L-p(I, E), J. Approx. Theory 116 (2002), 369-379]. Some examples and remarks related with N-simultaneous proximinality are also given.

Item Type:Article
Uncontrolled Keywords:Banach space.
Subjects:Sciences > Mathematics > Differential geometry
ID Code:16848

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