On a class of linear concurrence operators

摘要

Mean operators are often used to find a representative value for a collection of data. A new class of operators, in the same spirit as mean operators, called concurrence operators are then introduced which replace the idempotency condition by the stronger conditions of natural boundedness and self identity and removes the requirement of commutativity. A class of linear concurrence operators are then considered. The condition of self identity is shown to impose a strong requirement on the relationship between these operators for different cardinalities of arguments. This requirement allows us to define in a consistent manner noncommutative concurrence operators. A number of special cases are then considered.