Best Approximations in the Space of Bochner Integrable Functions
β Scribed by Dinh Quang Luu
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 305 KB
- Volume
- 121
- Category
- Article
- ISSN
- 0025-584X
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π SIMILAR VOLUMES
Let E be a Kothe function space over a complete measurable space and X a Banach space. Recall an element h in E is said to be order continuous if, for any Γ 4 < < decreasing sequence g in S , H g s 0 and g F h implies lim g s 0.
The object of this paper is to prove the following theorem: Let \(Y\) be a closed subspace of the Banach space \(X,(S, \Sigma, \mu)\) a \(\sigma\)-finite measure space, \(L(S, Y)\) (respectively, \(L(S, X)\) ) the space of all strongly measurable functions from \(S\) to \(Y\) (respectively, \(X\) ),
We show that the set of semi-Lipschitz functions, defined on a quasi-metric space (X, d ), that vanish at a fixed point x 0 # X can be endowed with the structure of a quasi-normed semilinear space. This provides an appropriate setting in which to characterize both the points of best approximation an