0. Introduction Let X be a real separable Banach space and X~* be its dual space, Let B(X) be the Borel field, i.e., the topological σ-field. A functional u: X→R’ is called a bounded smooth functional, if n∈N, f1,...0. Introduction Let X be a real separable Banach space and X~* be its dual space, Let B(X) be the Borel field, i.e., the topological σ-field. A functional u: X→R’ is called a bounded smooth functional, if n∈N, f1, …, fn∈ X~* and φ∈Cb~∞(Rn), such that展开更多
Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k greater than or equal to 2 be an integer and phi a weakly continuous linear surjective map from B(X) into itself. It is...Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k greater than or equal to 2 be an integer and phi a weakly continuous linear surjective map from B(X) into itself. It is shown that phi is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number lambda satisfying lambda(k-1) = 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - 1)-th power I.展开更多
文摘0. Introduction Let X be a real separable Banach space and X~* be its dual space, Let B(X) be the Borel field, i.e., the topological σ-field. A functional u: X→R’ is called a bounded smooth functional, if n∈N, f1, …, fn∈ X~* and φ∈Cb~∞(Rn), such that
基金The project is partially supported by NNSFC and PNSFS
文摘Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k greater than or equal to 2 be an integer and phi a weakly continuous linear surjective map from B(X) into itself. It is shown that phi is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number lambda satisfying lambda(k-1) = 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - 1)-th power I.
