Integral $K$-Operator Frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$

Abstract

In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from a Hilbert $C^{\ast}$-module $\mathcal{H}$ to itself denoted by $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $. We give some properties relating to some constructions of integral $K$-operator frames and to operators preserving integral $K$-operator frame and we establish some new results.

Keywords

• $k$-frames
• integral $k$-operator frames
• $c^{ast}$-algebra
• hilbert $mathcal{a}$-module