ON--半模空间中的一类范数及其单调性
ON a certain class of norms in semimodular spaces and their monotonicity properties
摘要：
设X是K上的线性空间，K=R或K=C，对n>1，ρ_i是定义在X上的s-凸半模，对任意i ∈ \in{1,...,n-1} .设ρ= \max_{1\leq i \leq n-1} \{ρ_i\}和X_ρ= { x \in X：ρ（dx）< \infty for some d >0 }。本文定义了X_ρ上一类新的s-范数（若s=1则为范数）。特别地，我们的定义以一种自然的方式推广了s-凸半模的Orlicz-Amemiya范数和Orlicz-Amemiya范数.然后，我们研究了半模空间的序连续性，Fatou性质和各种单调性。
英文摘要：
Let X be a linear space over K, K=R or K=C and let for n>1 ρ_i be s-convex semimodular defined on X for any i\in{1,...,n-1}. Put ρ=\max_{1\leq i \leq n-1}\{ρ_i\} and X_ρ= { x \in X: ρ(dx) < \infty for some d > 0 }. In this paper we define a new class of s-norms (norms if s=1) on X_ρ. In particular, our defintion generalizes in a natural way the Orlicz-Amemiya and Luxemburg norms defined for s-convex semimodulars. Then, we investigate order continuous, the Fatou Property and various monotonicity properties of semimodular spaces equipped with these s-norms.
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