Classification and geometrical propel Lies of the Xθ(•)-valued function spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Zhang, Qinghua¹  Li, Gang² 

[1] Nantong Univ, Dept Math, Nantong City 226007, Jiangsu, Peoples R China

[2] Yangzhou Univ, Dept Math, Yangzhou 225002, Jiangsu, Peoples R China

关键词: Bounded topological lattice;    Banach space net;    Continuous modular net;    Dual space net;    X-theta(center dot)-valued function space;    Geometrical property;   

DOI  :  10.1016/j.jmaa.2017.03.034

来源: Elsevier

【 摘 要 】

This paper is devoted to investigate the X-theta(.)-valued function spaces. Based on the notions of bounded topological lattice, Banach space net, continuous modular net and the dual space net, we divide X-theta(.)-valued function spaces into two classes: norm -modular spaces and modular -modular spaces. For the first class, we study the separability of L-+(p(.)), (I,X-theta(.)), give a representation of the dual space L-+(p(.)), (I,X-theta(.))*, find sufficient conditions of the equality L-+(p(.)), (I,X-theta(.)) = L-+(p(.)), (I,X-theta(.)), and prove the reflexivity of L-+(p(.)), (I,X-theta(.)) under some reasonable conditions. And for the second class, we prove the completeness and uniform convexity of L-+(p(.)), (I,X-theta(.)) in suitable situations. To show the naturality and rationality of these results,,t, some concrete function spaces such as L-+(p(+/-)), (I,L-p(x,L-t)(Omega)) L-pt(I, W-1,W-p(x,W-t)(Omega)), and L-pt L-pt(I, W-1,W-p(x,W-t)(Omega) together with L-pt(I, W-1,W-p(x,W-t)(Omega) are taken into account. (C) 2017 Elsevier Inc. All rights reserved.

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