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ISRN Applied Mathematics
Volume 2012 (2012), Article ID 251389, 13 pages
http://dx.doi.org/10.5402/2012/251389
Research Article

Maps Completely Preserving Involutions and Maps Completely Preserving Drazin Inverse

1College of Science, Harbin Engineering University, Harbin 150001, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
3East University of Heilongjiang, Harbin 150001, China

Received 24 August 2012; Accepted 2 October 2012

Academic Editors: H. Y. Chung and H. A. Larrondo

Copyright © 2012 Hongmei Yao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let and be infinite dimensional Banach spaces over the real or complex field , and let and be standard operator algebras on and , respectively. In this paper, the structures of surjective maps from onto that completely preserve involutions in both directions and that completely preserve Drazin inverse in both direction are determined, respectively. From the structures of these maps, it is shown that involutions and Drazin inverse are invariants of isomorphism in complete preserver problems.