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 $TXS^*-SX^*T^*= A$.

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

We construct an example of a Hilbert $$C^*$$ -module which shows that Troitsky’s theorem on the geometric essence $$ {\mathcal A} -compact operators between -modules cannot be extended to modules are not countably generated case (even in stronger uniform structure, is also introduced). In addition, constructed module admits no frames.

In this paper, we investigate the mapping of continuous g-frames in Hilbert C*-module under bounded operators. So, operators that preserve continuous g-frames in Hilbert C*-module were characterized. Then, we introduce equivalent continuous g-frames in Hilbert C*-module by the mapping of continuous g-frames in Hilbert C*-module under bounded operators. We show that every continuous g-frame in H...

Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C*-isomorphisms associated with projections introducing matched triple and semi-harmonious pair of projections. A (P, Q, H) is said be if H a Hilbert C*-module, P Q are on such that their infimum ∧ exists as an element $${\cal L}(H)$$ , where denotes set all adjointable operators H. The C*-subalgebras ...