IPM Calendar 
Saturday 25 June 2022   Today  
Events for day: Thursday 02 June 2022    
           11:00 - 13:00     Commutative Algebra Webinar
Generalized Drazin Invertibility of Anti-triangular Block Operator Matrices


Let X be a Banach space and B(X ) consists of all bounded linear operators on X . An operator T ∈ B(X ) is said to be generalized Drazin invertible, if there exists an operator S ∈ B(X ) such that, T S = ST, S = ST S, and T − T 2S is quasi − nilpotent. According to the research on singular differential equation, in 1983, Campbell investigated the relation between the Drazin inverse of the coefficient matrices of the differential equations and the solution of the differential equations. He proposed a problem to find an explicit representation of the Drazin inverse of block complex matrix ( E I F 0 ) . This ...