On the fine spectrum of the generalized difference operator over the sequence spaces and .
On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms
We deal with several classes of integral transformations of the form where is an operator. In case is the identity operator, we obtain several operator properties on with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on and define the inversion formula. Further, for an other class of differential operators of finite...
On the functions of one selfadjoint integral operator.
On the generalized Hardy spaces.
On the geometric properties of the joint spectrum of a family of self-adjoint operators
On the growth of Sobolev norms for the cubic Szegő equation
We report on a recent result establishing that trajectories of the cubic Szegő equation in Sobolev spaces with high regularity are generically unbounded, and moreover that, on solutions generated by suitable bounded subsets of initial data, every polynomial bound in time fails for high Sobolev norms. The proof relies on an instability phenomenon for a new nonlinear Fourier transform describing explicitly the solutions to the initial value problem, which is inherited from the Lax pair structure enjoyed...
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 Index of Callias-type Operators.
On the Index of Toeplitz Operators of Several Complex Variables.
On the integral operators of the third kind.
On the isomorphism of cartesian products of locally convex spaces
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 Kleinecke-Shirokov Theorem for families of derivations
It is proved that Riesz elements in the intersection of the kernel and the closure of the image of a family of derivations on a Banach algebra are quasinilpotent. Some related results are obtained.
On the largest analytic set for cyclic operators.
On the lattice boundary of Markov operators
On the lattice properties of invariant functions for Markov operators on C(X)
On the lattice structure of invariant functions for Markov operators on
On the limitations of the Grothendieck techniques.
On the Lipschitz operator algebras
In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an -Lipschitz operator from a compact metric space into a Banach space is defined and characterized in a natural way in the sence that is a -Lipschitz operator if and only if for each the mapping is a -Lipschitz function. The Lipschitz operators algebras and are developed here further, and we study their amenability and weak amenability of these algebras. Moreover, we prove an interesting result that and are isometrically...
On the local spectral properties of weighted shift operators
We study the local spectral properties of both unilateral and bilateral weighted shift operators.