 These two facts imply that "f" is continuous on "B" equipped with the weak topology, and "f" attains therefore its maximum "m" on "B" at some .By maximality, formula_20 which in turn implies that "y" also maximizes the Rayleigh quotient "g"("x") (see above).This shows that "y" is an eigenvector of "T", and ends the proof of the claim.