How to prove that <x, A*Ax> > 0 ?

ot tl @Ot-Tl

18 August 2015 1 5K Report

Let H1, H2 be Hilbert spaces and

A : H1 → H2 be a compact operator with the singular

system (λn, vn, un).

How to prove that > 0 where denotes the inner product ?

Igor Vestfrid

By the definition of the adjoint operator, = = ||Ax||2. Thus, > 0 provided x does not belong to the kernel of A and it is zero otherwise.

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