On Qian's problem for L_∞-spaces

2014/02/10 by Dai, Duanxu
#46B20 #54C60 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B04 #Secondary 46A22

paper · doi:10.48550/arxiv.1402.2123

Abstract

In this paper we devote to study Qian's problem for L_∞-spaces. Firstly, a positive answer to Qian's problem for C(K)-spaces is given by the assumption that K has the C\checkech-Stone property. Secondly, we obtain quantitative characterizations of separably injective spaces that turn out to give a positive answer to Qian's problem of 1995 in the setting of separable universality. Thirdly, we prove a sharpen quantitative and generalized Sobczyk theorem, which gives sharpen constants (α,γ) for Qian's Problem. Finally, we give a more generalized Figiel theorem for L_∞-spaces.

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