Representing as Elementary Operators Conditional Expectations on FW-Algebras
Xiao-Zhou Feng, Wenfeng Wang · Acta Analysis Functionalis Applicata · 2006
In this work, we define FW-algebras, which contain some special elements, and prove that if A is a FW-algebra, then we can give necessary and sufficient conditions for the minimal conditional expectation to be a faithful elementary conditional expectation of A. We give a description of all faithful elementary conditional expectations on FW-algebras. We then use these results to give necessary and sufficient conditions for certain conditional expectations to be index-finite and we derive an inequality for the index.