I sure hope it's a typo. (Otherwise I don't understand it either. :-)

I think it should indeed be [tex]\geq[/tex] , since otherwise it doesn't make sense
to "minimize" the ratio to get the eigenvalue. The [tex]\geq[/tex] is also what he
wrote in the previous Variational theorem on pp291-292.

Googling for "ballentine quantum errata" produced a few hits, but nothing
comprehensive, afaict. I sure wish Prof Ballentine and/or the publishers
would compile an errata list. One of the later chapters seemed to have
an elevated number or errors, as I recall. Maybe it didn't get good proofreading.