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Schur complements of selfadjoint Krein space operators
(Elsevier Science Inc, 2019-11)
Given a bounded selfadjoint operator W on a Krein space H and a closed subspace S of H, the Schur complement of W to S is defined under the hypothesis of weak complementability. A variational characterization of the Schur ...
Generalized Schur complements and oblique projections
(Elsevier Science Inc, 2002-01)
Let S be a closed subspace of a Hilbert space H and A a bounded linear selfadjoint operator on H. In this note, we show that the existence of A -selfadjoint projections with range S is related to some properties of shorted ...
Schur complements in Krein spaces
(Birkhauser Verlag Ag, 2007-12)
The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded) J-selfadjoint operator A (with the unique factorization property) acting on a Krein space H ...
A contractive version of a Schur–Horn theorem in II1 factors
(Elsevier, 2008-01)
We prove a contractive version of the Schur–Horn theorem for submajorization in II1 factors that complements some previous results on the Schur–Horn theorem within this context. We obtain a reformulation of a conjecture ...
Oblique projections and Schur complements
(University Szeged, 2001-01)
Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and ⟨,⟩_A : H x H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), ⟨ξ, n⟩_A =⟨Aξ, n⟩, ξ , n ∈ H. Given T∈ L(H), T is ...
On a class of non-Hermitian matrices with positive definite Schur complements
(American Mathematical Society, 2019-03)
Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite ...
On complementable operators in the sense of T. Ando
(Elsevier Science Inc, 2020-06)
Consider an operator A :H→K between Hilbert spaces and closed subspaces S ⊂ H and T ⊂ K. If there exist projections E on H and F on K such that R(E) =S, R(F) =T and AE=F∗A then A is called (S, T)-complementable. The origin ...
A preconditioner for the Schur complement matrix
(Elsevier, 2006-11)
A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a global problem in a narrow strip around the interface. ...