Some reverse inequalities for matrices on indefinite inner product spaces

In this paper, we generalize the following inequality due to N. Bebiano et al which states that for JJ-contraction T∈MnT∈Mn|[Tx,y]J|2≥[|T|J2αx,x]J[|T♯|J2(1−α)y,y]J for any x,y∈Cnx,y∈Cn with xx or yy time-like and α∈[0,1]α∈[0,1]. The above inequality gives a reverse weighted mixed Schwarz inequality. Also, we prove some reverse inequalities for indefinite inner product space. Moreover, we establish some refinements for the reverse of Schwarz inequality as well.