Re: Hilbert space inequality

In article <1167509227.754069.70200@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
PublicJY <pub_jy@xxxxxxxxx> wrote:
Suppose H is a complex Hilbert space, and A a linear operator from H
into H, and c a constant.
Prove that if (Ax, x) <= c ||x||^2 for all x in H then
|(Ax,y)| + | (Ay,x) | <= 2c ||x|| ||y|| for all x,y in H.

There is a counterexample when H is a real Hilbert space : the
rotation
of the plane by angle pi/2.

Counterexample for any Hilbert space: Ax = -x, c = 0.

Or did you mean -c ||x||^2 <= (Ax,x) <= c ||x||^2 ?

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.