Some estimates of certain subnormal and hyponormal derivations.
Some ideals of operators on Hilbert space
Some remarks on the uniform approximation property in Banach spaces
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 Concerning the M-Structure of Operator Spaces.
Some stable operator ideals
Some stable operator ideals.
Some stable operator ideals
Some variants of Anderson's inequality in -classes.
Some versions of Anderson's and Maher's inequalities. I.
Some versions of Anderson's and Maher's inequalities. II.
Spectral subspaces and non-commutative Hilbert transforms
Let G be a locally compact abelian group and ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. We study Hilbert transforms associated with G-flows on ℳ and closed semigroups Σ of Ĝ satisfying the condition Σ ∪ (-Σ) = Ĝ. We prove that Hilbert transforms on such closed semigroups satisfy a weak-type estimate and can be extended as linear maps from L¹(ℳ,τ) into . As an application, we obtain a Matsaev-type result for p = 1: if x is a quasi-nilpotent compact operator...
Spectre du noyau intégral
On construit les fonctions propres sur et les valeurs caractéristiques du noyau de Hilbert-Schmidt . Le spectre est donné par la solution d’une équation transcendante dont le comportement asymptotique est .
Splitting quasinorms and metric approximation properties
Strichartz inequality for orthonormal functions
We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation in a time-dependent potential and we show the existence of the wave operator in Schatten spaces.
Strictly Cosingular Operators on (DF)-Spaces.
Strongly exposed points in the unit ball of trace-class operators.
Structural properties of Banach and Fréchet spaces determined by the range of vector measures.
Subalgebras to a Wiener type algebra of pseudo-differential operators
We study general continuity properties for an increasing family of Banach spaces of classes for pseudo-differential symbols, where was introduced by J. Sjöstrand in 1993. We prove that the operators in are Schatten-von Neumann operators of order on . We prove also that and , provided . If instead , then . By modifying the definition of the -spaces, one also obtains symbol classes related to the spaces.