Controlled frame for operator in Hilbert \(\mathrm{C}^\ast \)-modules (Q2674235)

Summary: In this study, we will introduce a new concept, which is a controlled \(K\)-operator frame for the space of all adjointable operators on a Hilbert \(\mathcal{A} \)-module \(\mathcal{H}\) which denoted \(\operatorname{End}_{\mathcal{A}}^\ast\left(\mathcal{H}\right)\), where \(\mathcal{A}\) is a \(\mathrm{C}^\ast \)-algebra. Also, we establish some results of the controlled \(K\)-operator frame in \(\operatorname{End}_{\mathcal{A}}^\ast\left( \mathcal{H}\right)\). The presented results are new and of interest for people working in this area. Some illustrative examples are provided to advocate the usability of our results.