Sur les opérateurs bornés dans les espaces localement convexes
Sur quelques extensions au cadre banachique de la notion d'opérateur de Hilbert-Schmidt
In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operator: p-summing operators, γ-summing or γ-radonifying operators, weakly* 1-nuclear operators and classes of operators defined via factorization properties. We introduce the class PS₂(E;F) of pre-Hilbert-Schmidt operators as the class of all operators u: E → F such that w ∘ u ∘ v is Hilbert-Schmidt for every bounded operator v: H₁ → E and every bounded operator w: F → H₂, where H₁ and...
Sur une famille de cônes réticulés avec domination (les -cônes)
Il s’agit de représenter certains cônes réticulés par des cônes adaptés de fonctions continues sur un espace localement compact. Nous étudions le cône des opérateurs positifs majorés par un multiple de l’identité sur un cône réticulé, le représentons et donnons des conditions nécessaires et suffisantes pour qu’il soit riche (théorème d’Urysohn). Quelques illustrations sont données à la fin dans le cadre des espaces de type de Kakutani.
Surjective factorization of holomorphic mappings
We characterize the holomorphic mappings between complex Banach spaces that may be written in the form , where is another holomorphic mapping and belongs to a closed surjective operator ideal.
Symmetric stochastic matrices with given row sums.
Characterizations of extreme infinite symmetric stochastic matrices with respect to arbitrary non-negative vector r are given.
Symmetry breaking for molecular open systems
Tensor norms related to the space of Cohen p-nuclear multilinear mappings.
Tensor Product of Several Spaces and Nuclearity.
Tensor Products and Banach Ideals of p-Compact Operators.
Tensor products and elementary operators.
The algebra generated by a pair of operator weighted shifts
We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.
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 Bisognano-Wichmann theorem for charged states and the conformal boundary of a black hole.
The classical field limit of non-relativistic bosons. II. Asymptotic expansions for general potentials
The closure of the invertibles in a von Neumann algebra
In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman...
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 Feynman integral and Feynman's operational calculus: a heuristic and mathematical introduction
The Herz-Schur multiplier norm of sets satisfying the Leinert condition
It is well known that in a free group , one has , where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for .
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