On the Properties of Generalized Frames

In this paper, we introduce the notion of generalized frames and study their properties. Discrete and integral frames are special cases of generalized frames. We give criteria for generalized frames to be integral (discrete). We prove that any bounded operator $A$ with a bounded inverse acting from a separable space $H$ to $L_2(\Omega)$ (where $\Omega$ is a space with countably additive measure) can be regarded as an operator assigning to each element $x\in H$ its coefficients in some generalized frame.