Multiparameter spectral theory for weakly coupled operator system with bounded operators on a Hilbert tensor product space (Q2888343)

Let \(H_d^k\) be a direct sum of the separable Hilbert spaces \(H_j^k\), \(j = 1, 2, \dots, n\), and \(H = \bigotimes_{k=1}^n H_d^k\) be their Hilbert tensor product space. The spectral theory of the weakly coupled operator system \(A_kx_k = \sum_{j=1}^n \lambda_jC_{kj}x_k\), \(k = 1, 2, \dots, n\), with \(A_k = [A_{ij}^k]\), \(A_{ij}^k:H_j^k \rightarrow H_i^k\), \(C_{kj}:H_d^k \rightarrow H_d^k\), \(x_k\) being an \(n \times 1\) column vector, \(i,j,k = 1, 2, \dots, n\), is studied in this article.