A strict topology on Orlicz spaces

作者：Akbarbaglu I; Maghsoudi S; Seoane Sepulveda J B^*

来源：Mathematische Nachrichten, 2015, 288(5-6): 498-508.

DOI：10.1002/mana.201400100

• Young function
• Orlicz space
• strict topology
• locally compact group
• convolution
• Primary: 46E30
• 46A70
• 43A15
• Secondary: 46A03
• 46H05

Let phi be a Young function, be a locally compact space, and be a positive Radon measure on . We consider a strict topology phi (in the sense of Sentilles-Taylor) on the Orlicz function space M phi() and investigate various properties of this locally convex topology. We also study the Orlicz space M phi(G) of a locally compact group G with a left Haar measure under the strict topology phi and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on M phi(G) under the phi topology and other natural ones.

• 出版日期2015-4