LINEAR MAPS PRESERVING THE IDEMPOTENCY OF JORDAN PRODUCTS OF OPERATORS

作者：Fang Li^*

来源：Electronic Journal of Linear Algebra, 2011, 22: 767-779.

• Banach space
• Preserver
• Idempotent
• Jordan product

Let B(X) be the algebra of all bounded linear operators on a complex Banach space X and let I* (X) be the set of non-zero idempotent operators in B(X). A surjective map : B(X) -> B(X) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B is an element of B(X), the relation AB broken vertical bar BA is an element of I* (X)implies '(A)'(B) broken vertical bar '(B)'(A) is an element of I* (X). In this paper, the structures of linear surjective maps on B(X) preserving the nonzero idempotency of Jordan products of two operators are given.

• 出版日期2011-8
• 单位西北大学