群代数上的多重模与模
Multi-norms and modules over group algebras
摘要：
设G是局部紧群，且1 < p < \infty .本文研究了左L^1（G）-模L^p（G）的内射性.我们定义了一个顺从性类型的条件族，称为（p，q）-顺从性，对于任何1 <= p <= q。对一般的局部紧群G，证明了如果L^p（G）是内射的，则G必是（p，p）-顺从的.对于离散群G，我们证明了l^p（G）是单射的当且仅当G是（p，p）-顺从的.
英文摘要：
Let G be a locally compact group, and let 1 < p < \infty. In this paper we investigate the injectivity of the left L^1(G)-module L^p(G). We define a family of amenability type conditions called (p,q)-amenability, for any 1 <= p <= q. For a general locally compact group G we show if L^p(G) is injective, then G must be (p,p)-amenable. For a discrete group G we prove that l^p(G) is injective if and only if G is (p,p)-amenable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
