On Dominant Operators.
On Dominating Sequences in the Unit Disc.
On E. Borel's Theorem.
On eigenfunction expansions and scattering theory.
On Erb's uncertainty principle
We improve a result of Erb, concerning an uncertainty principle for orthogonal polynomials. The proof uses numerical range and a decomposition of some multiplication operators as a difference of orthogonal projections.
On ergodic properties of convolution operators associated with compact quantum groups
Recent results of M. Junge and Q. Xu on the ergodic properties of the averages of kernels in noncommutative -spaces are applied to the analysis of almost uniform convergence of operators induced by convolutions on compact quantum groups.
On ergodicity coefficients of infinite stochastic matrices.
On ergodicity for operators with bounded resolvent in Banach spaces
We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the operator A....
On essential selfadjointness of the Weyl quantized relativistic Hamiltonian.
On estimates for spectral projections of perturbed selfadjoint operators.
On existence of hyperinvariant subspaces for linear maps.
On existence of solutions to degenerate nonlinear optimization problems
We investigate the existence of the solution to the following problem min φ(x) subject to G(x)=0, where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.
On extended eigenvalues and extended eigenvectors of truncated shift
In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..
On factorization and partial indices of unitary matrix-functions of one class.
On Farkas-type theorems
On flatness and some ergodic properties of Banach spaces
On general Lipschitzian kernels.
On generalized a-Browder's theorem
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.
On generalized eigenfunctions of operators in a Hilbert space
On generalized inequalities of Heinz, Halmos and Bernstein.