EXISTENCE OF A KIND OF BEST SIMULTANEOUS APPROXIMATIONS IN $L_p(\Omega,\Sigma, X)$

Luo, X. F.; Peng, L. H.

doi:10.11650/twjm/1500406786

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“…These results are similar to [6]. However, in [6], more hypotheses are necessary and the proofs are totally different.…”

Section: Resultssupporting

confidence: 76%

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Best N-Simultaneous Approximation in Lp(μ,X)

Pakhrou

2017

Journal of Function Spaces

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Let X be a Banach space. Let 1≤p<∞ and denote by Lp(μ,X) the Banach space of all X-valued Bochner p-integrable functions on a certain positive complete σ-finite measure space (Ω,Σ,μ), endowed with the usual p-norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset W of X, the set Lp(μ,W) is N-simultaneously proximinal in Lp(μ,X) for any arbitrary monotonous norm N in Rn.

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“…These results are similar to [6]. However, in [6], more hypotheses are necessary and the proofs are totally different.…”

Section: Resultssupporting

confidence: 76%

“…The problem of the best -simultaneous approximation in ( , ) has been deeply and extensively studied; see, for example, [3][4][5][6][7][8][9][10][11]. When is a reflexive subspace of , it was proved in [3] that ( , ) is -simultaneously proximinal in ( , ), where is the Lebesgue measure on = [0, 1].…”

Section: Introductionmentioning

confidence: 99%