The solutions to some operator equations in Hilbert $C^*$-module

Author(s):

M. Mohammadzadeh Karizaki , M. Hassani *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.
Keywords:

Operator equation , Moore-Penrose inverse , Complemented submodule , Closed range , Hilbert C*-module

Language:
English
Published:
Journal of Linear and Topological Algebra, Volume:4 Issue: 1, Winter 2015
Pages:
35 to 42
https://www.magiran.com/p2262374