On proper boundary points of the spectrum and complemented eigenspaces.
On Pták’s generalization of Hankel operators
In 1997 Pták defined generalized Hankel operators as follows: Given two contractions and , an operator is said to be a generalized Hankel operator if and satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of and . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat...
On quasi-analytic vectors for some classes of operators
On quasi-compactness of operator nets on Banach spaces
The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net is equivalent to quasi-compactness of some operator . We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.
On Quasi-Normality of Two-Sided Multiplication
2000 Mathematics Subject Classification: 47B47, 47B10, 47A30.In this note, we characterize quasi-normality of two-sided multiplication, restricted to a norm ideal and we extend this result, to an important class which contains all quasi-normal operators. Also we give some applications of this result.
On quasiparabolical differential equations of higher order
On random evolutions induced by countable state space Markov chains
On real and complex spectra in some real -algebras and applications.
On reflexive subobject lattices and reflexive endomorphism algebras
In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.
On reflexivity and hyperreflexivity of some spaces of intertwining operators
Let be weak contractions (in the sense of Sz.-Nagy and Foiaş), the minimal functions of their parts and let be the greatest common inner divisor of . It is proved that the space of all operators intertwining is reflexive if and only if the model operator is reflexive. Here means the compression of the unilateral shift onto the space . In particular, in finite-dimensional spaces the space is reflexive if and only if all roots of the greatest common divisor of minimal polynomials...
On regular extensions of operator systems.
On regularities and Fredholm theory
We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.
On representation of linear operators on
On resonances in mathematical scattering theory
On Riesz and Inessential Operators.
On S. Mazur's problems 8 and 88 from the Scottish Book
The paper discusses Problems 8 and 88 posed by Stanisław Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Peller [J. Operator Theory 7 (1982)]. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper of Pełczyński and Sukochev in connection with Problem 88.
On semi-Fredholm operators and the conjugate of a product of operators
On semi-inner product spaces, I
On sequences off linear functionals and some operators of the class .
On solvability of the cohomology equation in function spaces
Let T be an endomorphism of a probability measure space (Ω,𝓐,μ), and f be a real-valued measurable function on Ω. We consider the cohomology equation f = h ∘ T - h. Conditions for the existence of real-valued measurable solutions h in some function spaces are deduced. The results obtained generalize and improve a recent result of Alonso, Hong and Obaya.