On Some New Inequalities For Continuous Fusion Frames in Hilbert Spaces

Continuous frames and fusion frames were considered recently as generalizations of frames in Hilbert spaces. In this paper, for any continuous fusion frame, we obtain a new family of inequalities which are parametrized by a parameter \(\lambda \in \mathbb {R}\). By suitable choices of \(\lambda \), one obtains the previous results as special cases. Moreover, these new inequalities involve the expressions \(\langle S_Yh,h \rangle \), \(\Vert S_Yh\Vert \), etc., where \(S_Y\) is a “truncated form” of the continuous fusion frame operator.