In this article we determine the eigenvalues of sequences of tridiagonal matrices that contain a Toeplitz matrix in the upper left block.

No abstract

Abstract. Let A, B be unital C * -algebras and P∞(A, B) be the set of all completely positive linear maps of A into B. In this article we characterize the extreme elements in P∞ (A, B, p) , p = Φ(1) for all Φ ∈ P∞(A, B, p), and pure elements in P∞(A, B) in terms of a self-dual Hilbert module structure induced by each Φ in P∞(A, B). Let P∞(B(H)) R be the subset of P∞(B(H), B(H)) consisting of R-module maps for a von Neumann algebra R ⊆ B(H).We characterize normal elements in P∞(B(H)) R to be extreme. Results here generalize various earlier results by Choi, Paschke and Lin.

Abstract. We give necessary and sufficient conditions for the sum of closed subspaces of a Hilbert space to be closed. Specifically, we show that the sum will be closed if and only if the angle between the subspaces is not zero, or if and only if the projection of either space into the orthogonal complement of the other is closed. We also give sufficient conditions for the sum to be closed in terms of the relevant orthogonal projections. As a consequence, we obtain sufficient conditions for the existence of an optimal solution to an abstract quadratic programming problem in terms of the kernels of the cost and constraint operators.2000 Mathematics Subject Classification. 46C05, 90C20.

No abstract