Some properties of strongly -decomposable operators.
Some properties of the sum of linear operators in the non-differential case.
Some properties of Van Koch's curves.
Some questions in operator theory and applications in analysis
Some Relations Between s-Numbers of Operators on Banach Spaces.
Some relations between Toeplitz and singular integral operators on odd spheres
Some remarks concerning the Large Sieve type
Some remarks on compact maps in Banach spaces
Some remarks on Gleason measures
This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.
Some remarks on orthomorphisms
Some remarks on polynomial operators
Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator
We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.
Some remarks on the invariant subspace problem for hyponormal operators.
Some remarks on the strong limit-point condition of second-order linear differential expressions
Some remarks on the surjectivity spectrum of linear operators
Some remarks on the uniform approximation property in Banach spaces
Some remarks on time-dependent evolution systems in the hyperbolic case
Some remarks on Toeplitz multipliers and Hankel matrices
Consider the set of all Toeplitz-Schur multipliers sending every upper triangular matrix from the trace class into a matrix with absolutely summable entries. We show that this set admits a description completely analogous to that of the set of all Fourier multipliers from H₁ into ℓ₁. We characterize the set of all Schur multipliers sending matrices representing bounded operators on ℓ₂ into matrices with absolutely summable entries. Next, we present a result (due to G. Pisier) that the upper triangular...
Some results about absolute summability of operators in Banach spaces.
In order to study the absolute summability of an operator T we consider the set ST = {{xn} | ∑||Txn|| < ∞}. It is well known that an operator T in a Hilbert space is nuclear if and only if ST contains an orthonormal basis and it is natural to ask under which conditions two orthonormal basis define the same left ideal of nuclear operators. Using results about ST we solve this problem in the more general context of Banach spaces.
Some results about dissipativity of Kolmogorov operators
Given a Hilbert space with a Borel probability measure , we prove the -dissipativity in of a Kolmogorov operator that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.