On precompact multiplication operators on weighted function spaces.
On representation of linear operators on
On restriction properties of multiplication operators.
On self-commutators of Toeplitz operators with rational symbols
We prove that the self-commutator of a Toeplitz operator with unbounded analytic rational symbol has a dense domain in both the Bergman space and the Hardy space of the unit disc. This is a basic step towards establishing whether the self-commutator has a compact or trace-class extension.
On the boundedness of Cauchy singular operator from the space to .
On the boundedness of the differentiation operator between weighted spaces of holomorphic functions
We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.
On the -characteristic of fractional powers of linear operators
We describe the geometric structure of the -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.
On the Composition Operator in AC[a,b].
Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.
On the composition operator in RVΦ [a,b].
On the computation of some quantities in the theory of Fredholm operators
On the convergence of the iterates of the Frobenius-Perron operator associated with a Markov map defined on an interval. The lower-function approach
On the Dunford-Pettis property
On the equivalence of differential operators of infinite order with constant coefficients
We investigate the conditions of equivalence of a differential operator of infinite order with constant coefficients to the operator of differentiation in one space of analytic functions. We also study the conditions of continuity of a differential operator of infinite order with variable coefficients in such space.
On the ergodic power function for invertible positive operators
On the essential order spectrum
On the functions of one selfadjoint integral operator.
On the Hardy-type integral operators in Banach function spaces.
Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.
On the integral operators of the third kind.
On the Kantorovich-Rubinstein maximum principle for the Fortet-Mourier norm
A new version of the maximum principle is presented. The classical Kantorovich-Rubinstein principle gives necessary conditions for the maxima of a linear functional acting on the space of Lipschitzian functions. The maximum value of this functional defines the Hutchinson metric on the space of probability measures. We show an analogous result for the Fortet-Mourier metric. This principle is then applied in the stability theory of Markov-Feller semigroups.
On the lattice boundary of Markov operators