Tensor products of almost r-summing maps.
Tensor Products of Weighted Bergman Spaces and Invariant Ha-Plitz Operators.
The associated tensor norm to -absolutely summing operators on -spaces
We give an explicit description of a tensor norm equivalent on to the associated tensor norm to the ideal of -absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to .
The -weak compactness of weak Banach-Saks operators
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
The behaviour of transformations on sequence spaces.
The boundary behaviour of -valued functions analytic in the half-plane with nonnegative imaginary part
The Cauchy-Riemann operator in infinite dimensional spaces.
The decomposability of operators relative to two subspaces
Let M and N be nonzero subspaces of a Hilbert space H satisfying M ∩ N = {0} and M ∨ N = H and let T ∈ ℬ(H). Consider the question: If T leaves each of M and N invariant, respectively, intertwines M and N, does T decompose as a sum of two operators with the same property and each of which, in addition, annihilates one of the subspaces? If the angle between M and N is positive the answer is affirmative. If the angle is zero, the answer is still affirmative for finite rank operators but there are...
The Grothendieck-Pietsch domination principle for nonlinear summing integral operators
We transform the concept of p-summing operators, 1≤ p < ∞, to the more general setting of nonlinear Banach space operators. For 1-summing operators on B(Σ,X)-spaces having weak integral representations we generalize the Grothendieck-Pietsch domination principle. This is applied for the characterization of 1-summing Hammerstein operators on C(S,X)-spaces. For p-summing Hammerstein operators we derive the existence of control measures and p-summing extensions to B(Σ,X)-spaces.
The ideal of p-compact operators: a tensor product approach
We study the space of p-compact operators, , using the theory of tensor norms and operator ideals. We prove that is associated to , the left injective associate of the Chevet-Saphar tensor norm (which is equal to ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that is equal to for a wide range of values of p and q, and show that our results are sharp....
The ideal property of tensor products of Banach lattices with applications to the local structure of spaces of absolutely summing operators
The laplacian and the Dirac operator in infinitely many variables
The moduli of smoothness and convexity and the Rademacher averages of the trace classes (1≤p<∞)
The Regularized Trace for Nuclear Perturbations of Discrete Operators
The Schur multiplication in tensor algebras
The S...-criterion for Hankel forms on the Fock space, 0 < p < 1.
The theorem on unitary equivalence of Fock representations
The trace class is a -algebra.
The trace of finite and nuclear elements in Banach algebras
Théorèmes de factorisation dans les espaces