On Sum of G-Frames in Hilbert Spaces

Abstract

We consider the sum of finite number of g-frames for a Hilbert space H and observed that their sum need not be a g-frame. A necessary and sufficient condition for the sum of two g-frames to be a g-frame has been obtained. Also, we study the sum of finite number of g-Bessel sequences and obtained some results regarding sum of g-Bessel sequences.

Key words and phrases. Fram, g-frame, g-Bessel sequence.

2000 Mathematics Subject Classification. 42C15, 42A38