Gram Operators of continuous frames in Hilbert spaces

In this note, we review and study continuous frames. In particular, for two given Bessel mappings $E$ and $F$, we define the so called cross-Gram operator $G_{E,F}$. We show that if $F$ and $G$ are Bessel mappings then $G_{E,F}$ is bounded. Also, we show that $G_{E,F}$ is bounded and invertible if and only if both $E$ and $F$ are of Riesz type.