On restriction properties of multiplication operators.
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 scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable -semigroups.
On scalar-valued nonlinear absolutely summing mappings
We investigate cases ("coincidence situations") in which every scalar-valued continuous n-homogeneous polynomial (or every continuous n-linear mapping) is absolutely (p;q)-summing. We extend some well known coincidence situations and obtain several non-coincidence results, inspired by a linear technique due to Lindenstrauss and Pełczyński.
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 smooth extensions of odd dimensional spheres and multidimensional Helton and Howe formula.
On some Banach ideals of operators
On some BK spaces.
On Some Classes Of Linear Equations
On some classes of linear equations.
On some classes of linear equations, II.
On some classes of Operators on Hilbert spaces
On some ergodic properties for continuous and affine functions
Two problems posed by Choquet and Foias are solved:(i) Let be a positive linear operator on the space of continuous real-valued functions on a compact Hausdorff space . It is shown that if converges pointwise to a continuous limit, then the convergence is uniform on .(ii) An example is given of a Choquet simplex and a positive linear operator on the space of continuous affine real-valued functions on , such thatfor each in , but does not converge to 0.
On some matrix Inequalities in Banach Spaces
On some new embedding theorems for some analytic classes in the unit ball.
On Some Operator Inequalities.
On some problems connected with diagonal map in some spaces of analytic functions
For any holomorphic function on the unit polydisk we consider its restriction to the diagonal, i.e., the function in the unit disc defined by , and prove that the diagonal map maps the space of the polydisk onto the space of the unit disk.
On some properties of holomorphic spaces based on Bergman metric ball and Luzin area operator.
On some spectral properties of Radon-Nicolski operations and their generalizations