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    STUDIA MATHEMATICA - Issue no. 4 / 2019  
         
  Article:   ASCENT, DESCENT AND ADDITIVE PRESERVING PROBLEMS.

Authors:  MOURAD OUDGHIRI, KHALID SOUILAH. 		 
       
         
  Abstract:  Given an integer n ³ 1, we provide a complete description of all additive surjective maps, on the algebra of all bounded linear operators acting on a complex separable infinite-dimensional Hilbert space, preserving in both directions the set of all bounded linear operators with ascent (resp. descent) nongreater than n. In the context of Banach spaces, we consider the additive preserving problem for semi-Fredholm operators with ascent or descent non-greater than n.

Mathematics Subject Classification (2010): 47B49, 47L99, 47A55, 47B37.

Keywords: Linear preserver problems, ascent, descent, semi-Fredholm operators.
 
         
     
         
         
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