Jordan homomorphisms and derivations on algebras of measurable operators

• Main Author: Weigt, Martin
• Other Authors: Conradie, JJ
• Format: Doctoral Thesis
• Language: English
• Published: University of Cape Town 2014
• Subjects: Mathematics and Applied Mathematics
• Online Access: http://hdl.handle.net/11427/4944

Includes abstract. === Includes bibliographical references (p.122-132) and index. === A few decades ago, Kaplansky raised the question whether unital linear invertibility preserving maps between unital algebras are Jordan homomorphisms. This question is still unanswered, and the progress that has been made has mainly been in the context of Banach algebras, including C*-algebras and von Neumann algebras. Let M be a von Neumann algebra with a faithful semifinite normal trace τ , and M~ the algebra of τ-measurable operators (measurable for short) affiliated with M. The algebra M~ can be endowed with a topology Уcm, called the topology of convergence in measure, such that M~ becomes a complete metrizable topological *-algebra in which M is dense. One of the aims of this thesis is to find answers to Kaplansky’s question in the context of algebras of measurable operators.