Let B(X) be the algebra of bounded operators on a complex infinite dimensional Banach space X, and F (X) be the subalgebra of all finite rank operators in B(X). A characterization of additive mappings on F (X) which preserve rank one nilpotent operators in both directions is given. As applications o
Additive Maps Preserving Nilpotent Operators or Spectral Radius
β Scribed by Zhao Fang Bai; Jin Chuan Hou
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2005
- Tongue
- English
- Weight
- 255 KB
- Volume
- 21
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let X be a complex Banach space. If 8: B(X) Γ B(X) is a surjective linear map such that A and 8(A) have the same spectral radius for every A # B(X), then 8=c3 where 3 is either an algebra-automorphism or an antiautomorphism of B(X) and c is a complex constant such that |c|=1.
Let L(H) be the algebra of all bounded linear operators on an infinite dimensional complex Hilbert H. We characterize linear maps from L(H) onto itself that preserve the essential spectral radius.
Define the sign-real spectral radius of a real n Γ n matrix A as Ο s 0 (A) = max SβS Ο 0 (SA), where Ο 0 (A) = max{|Ξ»|; Ξ» a real eigenvalue of A} is the real spectral radius of A and S denotes the set of signature matrices, i.e. S = {S; |S| = I}, the absolute value of matrices being meant entrywise.