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Journal of Operator Theory

Volume 71, Issue 1, Winter 2014  pp. 63-83.

Additive preservers of the ascent, descent and related subsets

Authors Mostafa Mbekhta (1), Vladimir Muller (2), and Mourad Oudghiri (3)
Author institution: (1) UFR de Mathematiques, Universite Lille1, Villeneuve Cedex, 59655, France
(2) Mathematical Institute, Czech Academy of Sciences Zitna 25, Prague 1, 11567, Czech Republic
(3) Laboratoire LAGA Faculte des Sciences, Universite Mohammed Premier, Oujda, 60000, Morocco

Summary:  In this paper we completely describe additive surjective continuous maps in the algebra of all bounded linear operators acting on a complex separable infinite-dimensional Hilbert space, preserving the operators of finite ascent, the operators of finite descent, Drazin invertible operators, upper semi-Browder operators, lower semi-Browder operators or Browder operators in both directions.

Keywords:  additive preservers, ascent, descent, Browder

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