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.
Some Results Concerning the M-Structure of Operator Spaces.
Some results on composition operators on .
Some results on dominant operators.
Some results on duality for spectral decompositions
Some results on order weakly compact operators
We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.
Some results on (strong) asymptotic Toeplitzness and Hankelness
Based on the results in A. Feintuch (1989), this work sheds light upon some interesting properties of strongly asymptotically Toeplitz and Hankel operators, and relations between these two classes of operators. Indeed, among other things, two main results here are (a) vanishing Toeplitz and Hankel operators forms an ideal, and (b) finding the distance of a strongly asymptotically Toeplitz operator from the set of vanishing Toeplitz operators.
Some results on the class of -unbounded Dunford-Pettis operators
We introduce and study the class of unbounded Dunford--Pettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.
Some spectral inequalities involving generalized scalar operators
In 1971, Allan Sinclair proved that for a hermitian element h of a Banach algebra and λ complex we have ∥λ + h∥ = r(λ + h), where r denotes the spectral radius. Using Levin's subordination theory for entire functions of exponential type, we extend this result locally to a much larger class of generalized spectral operators. This fundamental result improves many earlier results due to Gelfand, Hille, Colojoară-Foiaş, Vidav, Dowson, Dowson-Gillespie-Spain, Crabb-Spain, I. & V. Istrăţescu, Barnes,...
Some stable operator ideals
Some stable operator ideals.
Some stable operator ideals
Some Steinhaus type theorems over valued fields
Some subnormal Toeplitz operators.
Some type of rotational scheme.
Some variants of Anderson's inequality in -classes.