Sequential regularization of ill-posed problems involving unbounded operators
Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
Shift-invariant functionals on Banach sequence spaces
The present paper is a continuation of [23], from which we know that the theory of traces on the Marcinkiewicz operator ideal can be reduced to the theory of shift-invariant functionals on the Banach sequence space . The final purpose of my studies, which will be finished in [24], is the following. Using the density character as a measure, I want to determine the size of some subspaces of the dual *(H). Of particular interest are the sets formed by the Dixmier traces and the Connes-Dixmier traces...
Singular Value Estimates for Certain Convolution-Product Operators.
Small ideals of operators
Smooth operators in the commutant of a contraction
For a completely non-unitary contraction T, some necessary (and, in certain cases, sufficient) conditions are found for the range of the calculus, , and the commutant, T’, to contain non-zero compact operators, and for the finite rank operators of T’ to be dense in the set of compact operators of T’. A sufficient condition is given for T’ to contain non-zero operators from the Schatten-von Neumann classes .
s-numbers, eigenvalues and the trace theorem in Banach spaces
s-numbers of diagonal operators and Besov embeddings
s-Numbers of operators in Banach spaces
Sobre la estructura de los espacios de operadores de Lorentz.
Sobre la topología débil en componentes del ideal de los operadores p-compactos de Saphar con 1 < p < ∞.
Some applications of p-summing operators to Banach space theory
Some Characterizations of AM- and AL-Spaces.
Some duality results on bounded approximation properties of pairs
The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair has the λ-bounded approximation property. Then there exists a net of finite-rank operators on X such that and for all α, and and converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
Some Estimates for Type and Cotype Constants.
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.