| Additive Maps Preserving Nilpotent Operators or Spectral Radius |
| |
| 引用本文： | Zhao Fang BAI Jin Chuan HOU. Additive Maps Preserving Nilpotent Operators or Spectral Radius[J]. 数学学报(英文版), 2005, 21(5): 1167-1182. DOI: 10.1007/s10114-005-0503-y |
| |
| 作者姓名： | Zhao Fang BAI Jin Chuan HOU |
| |
| 作者单位： | [1]School of Science, Xi＇an Jiaotong University, Xi＇an 710049, P. R. China [2]Department of Mathematics, Shanxi Teachers University, Linfen 041004, P. R. China |
| |
| 基金项目： | This work is supported by NNSFC and PNSFS |
| |
| 摘 要： | Let X be a （real or complex） Banach space with dimension greater than 2 and let B0（X） be the subspace of B（X） spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Ф on B0（X） which preserve nilpotent operators in both directions. In particular, if X is infinite-dimensional, we prove that Ф has the form either Ф（T） = cATA^-1 or Ф（T） = cAT＇A^-1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T＇ denotes the adjoint of T. As an application of these results, we show that every additive surjective map on B（X） preserving spectral radius has a similar form to the above with ｜c｜ = 1.
|
| 关 键 词： | 附加保护 幂算子 光谱范围 Banach空间 子空间 |
| 收稿时间： | 2003-06-04 |
| 修稿时间： | 2003-06-042003-08-06 |
Additive Maps Preserving Nilpotent Operators or Spectral Radius |
| |
| Zhao Fang Bai,Jin Chuan Hou. Additive Maps Preserving Nilpotent Operators or Spectral Radius[J]. Acta Mathematica Sinica(English Series), 2005, 21(5): 1167-1182. DOI: 10.1007/s10114-005-0503-y |
| |
| Authors: | Zhao Fang Bai Jin Chuan Hou |
| |
| Affiliation: | (1) School of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China;(2) Department of Mathematics, Shanxi Teachers University, Linfen 041004, P. R. China;(3) Department of Mathematics, Shanxi Teachers University, Linfen 041004, P. R. China |
| |
| Abstract: | Let X be a (real or complex) Banach space with dimension greater than 2 and let ℬ0(X) be the subspace of ℬ(X) spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Φ on ℬ0(X) which preserve nilpotent operators in both directions. In particular, if X is infinite–dimensional, we prove that Φ has the form either Φ(T) = cATA −1 or Φ(T) = cAT'A −1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T' denotes the adjoint of T. As an application of these results, we show that every additive surjective map on ℬ(X) preserving spectral radius has a similar form to the above with |c| = 1. This work is supported by NNSFC and PNSFS |
| |
| Keywords: | Additive preservers Nilpotent operators Spectral radius |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
