On the equations X=KXS and AX=XK
On the invariant subspace problem in Banach spaces
On the orbit of the centralizer of a matrix
Let A be a complex n × n matrix. Let A' be its commutant in Mₙ(ℂ), and C(A) be its centralizer in GL(n,ℂ). Consider the standard C(A)-action on ℂⁿ. We describe the C(A)-orbits via invariant subspaces of A'. For example, we count the number of C(A)-orbits as well as that of invariant subspaces of A'.
On the reflexivity and hyperreflexivity of algebras and subspaces
A review of recent reflexivity and hyperreflexivity results is presented. We concentrate particularly on a finite-dimensional situation, Toeplitz operators and partial isometries. Open problems in this area are given.
On the reflexivity of multigenerator algebras [Book]
On the spectral radius of positive operators.
On the spectral radius of positive operators (Corrigendum).
On triangularization of algebras of operators.
On unitary equivalence of invariant subspaces of the Dirichlet space
It is shown that in the Dirichlet space , two invariant subspaces ℳ ₁, ℳ ₂ of the Dirichlet shift are unitarily equivalent only if ℳ ₁ = ℳ ₂.
Operator models and Arveson's curvature invariant
Operator positivity and analytic models of commuting tuples of operators
We study analytic models of operators of class with natural positivity assumptions. In particular, we prove that for an m-hypercontraction on a Hilbert space , there exist Hilbert spaces and ⁎ and a partially isometric multiplier θ ∈ ℳ (H²(),A²ₘ(⁎)) such that and , where A²ₘ(⁎) is the ⁎-valued weighted Bergman space and H²() is the -valued Hardy space over the unit disc . We then proceed to study analytic models for doubly commuting n-tuples of operators and investigate their applications...
Operators with rich invariant subspace lattices.
Periodic solutions of partial differential equations with hysteresis
Perturbations of Selfadjoint Operators with Point Spectra by Restrictions and Selfadjoint Extensions.
Proper contractions and invariant subspaces.
Propriétés spectrales des restrictions d’opérateurs de la classe
Quadratic operators and invariant subspaces
Quasiaffine transforms of operators
We obtain a new sufficient condition (which may be useful elsewhere) that a compact perturbation of a normal operator be the quasiaffine transform of some normal operator. We also give some applications of this result.
Quasi-invariant subspaces generated by polynomials with nonzero leading terms
We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].
Quasireducible operators.