Hermitian solutions to the system of operator equations T_iX=U_i.

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

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 $TXS^*-SX^*T^*= A$.

Evolution System Approximations of Solutions to Closed Linear Operator Equations

ABSTRACT. With S a linearly ordered set with the least upper bound property, with g a nonincreasing real-valued function on S, and with A a densely denned dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation M(s, i)x = x + A((L)[sdgM(-, t)x). An affine version of this equation is also considered. Under the hypothesis that the evolufion...

the solutions to some operator equations in hilbert c*-module

in this paper, we state some results on product of operators with closed rangesand we solve the operator equation txs*- sx*t*= a in the general setting of theadjointable operators between hilbert c*-modules, when ts = 1. furthermore, by usingsome block operator matrix techniques, we nd explicit solution of the operator equationtxs*- sx*t*= a.

On the eigenvalue decay of solutions to operator Lyapunov equations

This paper is concerned with the eigenvalue decay of the solution to operator Lya-punov equations with right-hand sides of finite rank. We show that the kth eigenvalue decays exponentially in √ k, provided that the involved operator A generates an exponentially stable continuous semigroup, and A is either self-adjoint or diagonalizable. Numerical experiments with discretizations of 1D and 2D PD...

G-positive and G-repositive solutions to some adjointable operator equations over Hilbert C^{∗}-modules

Some necessary and sufficient conditions are given for the existence of a G-positive (G-repositive) solution to adjointable operator equations $AX=C,AXA^{left( astright) }=C$ and $AXB=C$ over Hilbert $C^{ast}$-modules, respectively. Moreover, the expressions of these general G-positive (G-repositive) solutions are also derived. Some of the findings of this paper extend some known results in the...

Hypergeometric series solutions of linear operator equations