Indicial equivalents of multiparameter definiteness conditions in finite dimensions

Abstract

Let Tm, Vmn be Hermitean linear operators on complex Hilbert spaces Hm, m=1…k. A nonzero column vector satisfyingwill be called an eigenvalue. This type of problem has been studied extensively by Atkinson [2] from the viewpoint of determinantal operators on the tensor product We shall connect his work with more recent investigations [5,7] of eigenvalue indices based on minimax principles for , which can be viewed as an operator on .