Related papers: The invertibility of 2X2 operator matrices

A classification of commutative integral domains consisting of ordinary differential operators with matrix coefficients is established in terms of morphisms between algebraic curves.

In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…

In this work we study the following three space problem for operator spaces: if X is an operator space with base space isomorphic to a Hilbert space and X contains a completely isomorphic copy of the operator Hilbert space OH with…

We characterize matrix-valued asymmetric truncated Toeplitz operators (which are compressions of multiplication operators acting between two possibly different model spaces) by using compressed shifts, modified compressed shifts and shift…

Random matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what is the probability that it will have a…

We characterize the idempotent stable range one $2\times 2$ matrices over commutative rings and in particular, the integral matrices with this property. Several special cases and examples complete the subject.

A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a…

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation…

The discrete Lax operators with the spectral parameter on an algebraic curve are defined. A hierarchy of commuting flows on the space of such operators is constructed. It is shown that these flows are linearized by the spectral transform…

We consider a tensor product of two spaces of holomorphic functions on a Hermitian symmetric space of tube type. Then generically this is decomposed into a direct sum of irreducible subrepresentations. In this manuscript, we construct the…

We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…

We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…

A new class of infinite-dimensional Lie algebras given a name of Lax operator algebras, and the related unifying approach to finite-dimensional integrable systems with spectral parameter on a Riemann surface, such as Calogero--Moser and…

We discuss the reflexivity of hyperexpansions and their Cauchy dual operators. In particular, we show that any cyclic completely hyperexpansive operator is reflexive. We also establish the reflexivity of the Cauchy dual of an arbitrary…

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…

We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…

We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…

Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry…

We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of…

Asymmetric dual truncated Toeplitz operators acting between the orthogonal complements of two (eventually different) model spaces are introduced and studied. They are shown to be equivalent after extension to paired operators on…