Title of article :
The Solution of Operator Equations 𝑨 𝑿 𝑩 + 𝑿^∗ = 𝑪 𝑨 𝑿 𝑩 + 𝑩^∗𝑿^∗ 𝑪 = 𝑫
Author/Authors :
ahmeadp, buthainah a. baghdad university - college of science - department of mathematics, Iraq , ibraheam, noor e. baghdad university - college of science - department of mathematics, Iraq
Abstract :
In this paper, we study the solvability of two operator equations 𝐴 𝑋 𝐵 + 𝑋^∗ = 𝐶 (1) and 𝐴 𝑋 𝐵 + 𝐵^∗𝑋^∗𝐶 = 𝐷 (2) Where A, B, C and D are bounded linear operators. We give the necessary and sufficient conditions for the existence of a solution of equation (1), and describe the general form of the solution in the solvable case for both equations by using g-inverse of the operator B.
Keywords :
Operator equation , Moore , penrose inverse
Journal title :
Iraqi Journal Of Science
Journal title :
Iraqi Journal Of Science
