Weighted binary relations for operators on Banach spaces

Abstract

Using the Wg-Drazin inverses, we introduce and characterize new weighted preorders on the set of all bounded linear operators between two Banach spaces. As an application, we present two generalized Drazin pre-orders and an extension of the generalized Drazin order to a partial order.Mathematics Subject Classification. 47A05, 47A99, 15A09.

On the minus partial order in control systems

“…Proposition 14. Consider the ordered systems (M, B) and (M + BF, B) with M as in (8) satisfying the condition given in (15).…”

“…In particular, the minus partial order plays an important role in solving problems that involve shorted operators or modified matrices by adding/deleting a row or a column [8,14]. Some results on theoretical, applied, and numerical aspects of generalized inverses and partial orders can be found in [6,7,9,15,16,17,19,20,21].…”

“…Let (M, B) be a compartmental system with M structured as in(8) satisfying the condition(15) andB = O B 2 such that rank(B 2 ) = m.…”

Weighted G-Drazin inverses and a new pre-order on rectangular matrices

“…For a most extensive study on generalized inverses, matrix partial orders, and pre-orders the authors refer the reader to [1,2,3,6,7,10,12,13,14,18,19,20,21,22,24,26].…”

Nilpotent matrices and the minus partial order

“…However, to our acknowledge, the minus partial order for nilpotent matrices has not been investigated and it will be partially considered in this paper. In [8,9] similar relations to Drazin preorder were studied for rectangular matrices, and then extended to operators on Banach spaces in [4,11].…”