A Kowalski–S?odkowski theorem for 2-local \(^*\) -homomorphisms on von Neumann algebras

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• 作者：Maria Burgos ; Francisco J. Fernández-Polo…
• 关键词：Local homomorphism ; Local $$^*$$ ?homomorphism ; 2 ; Local homomorphism ; 2 ; Local $$^*$$ ?homomorphism ; 2 ; Local automorphism ; 2 ; Local $$^*$$ ?automorphism ; Primary 47B49 ; 46L40 ; 46L57 ; 47B47 ; 47D25 ; 47A ; 15A99 ; 16S50 ; 47L30
• 刊名：Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：109
• 期：2
• 页码：551-568
• 全文大小：508 KB
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• 作者单位：Maria Burgos (1)
  Francisco J. Fernández-Polo (2)
  Jorge J. Garcés (2)
  Antonio M. Peralta (2) (3)
  
  1. Departamento de Matematicas, Facultad de Ciencias Sociales y de la Educacion, Universidad de Cadiz, 11405, Jerez de la Frontera, Spain
  2. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain
  3. Department of Mathematics, College of Science, King Saud University, P.O.Box 2455-5, Riyadh, 11451, Kingdom of Saudi Arabia
  
• 刊物类别：Mathematics and Statistics
• 出版者：Springer Milan
• ISSN：1579-1505

文摘

It is established that every (not necessarily linear) 2-local \(^*\)-homomorphism from a von Neumann algebra into a C\(^*\)-algebra is linear and a \(^*\)-homomorphism. In the setting of (not necessarily linear) 2-local \(^*\)-homomorphism from a compact C\(^*\)-algebra we prove that the same conclusion remains valid. We also prove that every 2-local Jordan \(^*\)-homomorphism from a JBW\(^*\)-algebra into a JB\(^*\)-algebra is linear and a Jordan \(^*\)-homomorphism.