Another positivity result for determinantal operators
Paul Binding · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1980
Synopsis Let Vrs, s = 1 … k, be Hermitian operators on separable Hilbert spaces Hr, r = 1 … k. For x⊗ = x1⊗ … ⊗ xk ∈ H = H1⊗…Δx⊗ by the formal determinantal expansion ⊗ det [Vrsxr Δ is then extended by linearity and continuity to H. It is shown that a positive definiteness condition on Δ need be checked only for decomposable tensors like x⊗. Applications are given to several conditions in the multiparameter eigenvalue literature.