71 citations · 138 across the 9 of their papers we have counts for
6 papers · 1 filter
The singularly continuous spectrum and non-closed invariant subspaces
Vadim Kostrykin, Konstantin A. Makarov
Let be a bounded self-adjoint operator on a separable Hilbert space and a closed invariant subspace of .…
A generalization of the Theorem
Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov
Let be a bounded self-adjoint operator on a separable Hilbert space and a closed invariant subspace of .…
On the existence of solutions to the operator Riccati equation and the tanΘtheorem
Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov
Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d>0 be the distance between the spectra of A and C. We prove that under…
Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach
Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov
We introduce a new concept of unbounded solutions to the operator Riccati equation and give a complete description of its solutions associated…
On a Subspace Perturbation Problem
Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov
We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let and be bounded self-adjoint operators. Assu…
Concavity of Eigenvalue Sums and the Spectral Shift Function
Vadim Kostrykin
It is well known that the sum of negative (positive) eigenvalues of some finite Hermitian matrix is concave (convex) with respect to . Using the theory of the spectral shift…