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Involutions on the second duals of group algebras and a multiplier problem

Farhadi, H ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1017/S0013091505000660
  3. Publisher: 2007
  4. Abstract:
  5. We show that if a locally compact group G is non-discrete or has an infinite amenable subgroup, then the second dual algebra L1(G) ** does not admit an involution extending the natural involution of L1(G). Thus, for the above classes of groups we answer in the negative a question raised by Duncan and Hosseiniun in 1979. We also find necessary and sufficient conditions for the dual of certain left-introverted subspaces of the space Cb(G) (of bounded continuous functions on G) to admit involutions. We show that the involution problem is related to a multiplier problem. Finally, we show that certain non-trivial quotients of L1(G)** admit involutions
  6. Keywords:
  7. Primary 43A20 ; Weakly almost periodic function ; Left uniformly continuous function ; Multiplier ; Involution ; Arens product ; Amenable group ; Secondary 46K99 ; 43A22
  8. Source: Proceedings of the Edinburgh Mathematical Society ; Volume 50, Issue 1 , 2007 , Pages 153-161 ; 00130915 (ISSN)
  9. URL: https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/involutions-on-the-second-duals-of-group-algebras-and-a-multiplier-problem/0187CE60115C52AD0E960FAE0DC926F5