Factoring Operators Through Banach Lattices Not Containing C(0, 1).
Factoring Operators through c0 .
Factoring Rosenthal operators.
In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l1.
Factoring the identity operator on a subspace of
Factoring unconditionally converging operators
Factorisation des applications -sommantes
Factorisation des isomorphies d’ordre des espaces
Factorisation d'opérateurs différentiels à coefficients rationnels
Factorization and domination of positive Banach-Saks operators
It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.
Factorization and extension of positive homogeneous polynomials
We study the following problem: Given a homogeneous polynomial from a sublattice of a Banach lattice to a Banach lattice, under which additional hypotheses does this polynomial factorize through -spaces involving multiplication operators? We prove that under some lattice convexity and concavity hypotheses, for polynomials certain vector-valued norm inequalities and weighted norm inequalities are equivalent. We combine these results and prove a factorization theorem for positive homogeneous polynomials...
Factorization and extrapolation of pairs of weights
Factorization by Lattice Homomorphisms.
Factorization of compact operators and applications to the approximation problem
Factorization of compact operators and finite representability of Banach spaces with applications to Schwartz spaces
Factorization of entropy ideals: proportional case
Factorization of -quasihyponormal operators.
Factorization of Montel operators
Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.
Factorization of operators and weighted norm inequalities
Factorization of operators on C*-algebras
Let A be a C*-algebra. We prove that every absolutely summing operator from A into factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and with , then for every ε >0, the ε-capacity of...
Factorization of Operators Through Lp ... or Lp1 and Non-Commutative Generalizations.