Nonlinear maps preserving semi-Fredholm operators with finite ascent

Key Points

• The aim is to classify nonlinear maps that maintain the properties of semi-Fredholm operators with bounded ascent.
• Characterization of nonlinear maps on B(X) that uphold the semi-Fredholm operator status.
• Focus on operators within infinite-dimensional complex Banach spaces.
• Detailed structure of nonlinear maps preserving semi-Fredholm operators is fully described.
• Preservation of ascent constraints and their implications are established.