The general solution to a system of adjointable operator equations over Hilbert C^∗-modules
نویسندگان
چکیده
منابع مشابه
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...
متن کاملg-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...
متن کاملEla Positive and Re-positive Solutions to Some Systems of Adjointable Operator Equations over Hilbert C−modules∗
A necessary and sufficient condition for the existence of the general common positive solution to equations A1X = C1, XB2 = C2, A3XA ∗ 3 = C3, A4XA ∗ 4 = C4 for operators between Hilbert C-modules is established, and an expression for the common positive solution to the equations is derived when the solvability conditions are satisfied. As an application, a new necessary and sufficient conditio...
متن کاملThe 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 $TXS^*-SX^*T^*= A$.
متن کاملThe solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules
In this paper, we find explicit solution to the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2011
ISSN: 1846-3886
DOI: 10.7153/oam-05-24