Some results on controlled frames in hilbert spaces

We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We introduce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.