TY - JOUR
ID - 4059
TI - Hermitian solutions to the system of operator equations T_iX=U_i.
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Vaezpour, S.Mansour
AU - Bakhtiari, Zahra
AD - Amirkabir University of Technology (Tehran Polytechnic)
AD - Department of Mathematics, Payam e Nour University, Tehran, Iran
Y1 - 2019
PY - 2019
VL - 10
IS - 1
SP - 139
EP - 152
KW - Operator equation
KW - Hermitian solution
KW - Common solution
KW - Existence of solution
KW - Moore penrose inverse
DO - 10.22075/ijnaa.2017.1475.1378
N2 - In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then give the general form of common Hermitian solutions to this system of equations. Cosequently, we give the necessary and sffcient conditions for the existence of common Hermitian solutions to the system of operator equati and also present the necessary conditions for solvability of the equation sum_{i=1}{n}T_iX_i=U
UR - https://ijnaa.semnan.ac.ir/article_4059.html
L1 - https://ijnaa.semnan.ac.ir/article_4059_01638be695de3fa1c98b915e397bc3bf.pdf
ER -