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 J - contraction T is an element of M-n vertical bar[Tx, y](J)vertical bar(2) >= [vertical bar T vertical bar(2 alpha)(J) x,x](J) [vertical bar T-#vertical bar(2(1-alpha))(J) y,y](J) for any x, y is an element of C-n with x or y time-like and alpha is an element of [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. (C) 2015 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.