LAUSR

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 $$\lambda \in \mathbb {R}$$λ∈R. By suitable choices of $$\lambda $$λ, one obtains the previous results as special cases. Moreover, these new inequalities involve the expressions $$\langle S_Yh,h \rangle $$⟨SYh,h⟩, $$\Vert S_Yh\Vert $$‖SYh‖, etc., where $$S_Y$$SY is a “truncated form” of the continuous fusion frame operator.