The Bessaga-Pelczynski Property and Strongly Bounded Measures
The best constants in the Khintchine inequality
The bidual of a tensor product of Banach spaces.
This paper studies the relationship between the bidual of the (projective) tensor product of Banach spaces and the tensor product of their biduals.
The bidual of the space of polynomials on a Banach space.
The Bishop-Phelps-Bollobás property for numerical radius in ℓ₁(ℂ)
We show that the set of bounded linear operators from X to X admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever X is ℓ₁(ℂ) or c₀(ℂ). As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ℓ₁(ℂ).
The bottleneck conjecture.
The bounded approximation property for the predual of the space of bounded holomorphic mappings
When U is the open unit ball of a separable Banach space E, we show that , the predual of the space of bounded holomorphic mappings on U, has the bounded approximation property if and only if E has the bounded approximation property.
The bounded approximation property for weakly uniformly continuous type holomorphic mappings.
The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces
The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space.
The boundedness principle for lattice-normed spaces.
The Cartan-Thullen theorem for Banach spaces
The Centralizer of Bochner L°°-Spaces.
The chain rule for differentiable measures
The characteristic of weak convergence on Banach sequence lattices.
A sufficient and necessary condition for weak convergence of sequences in a class of Banach sequence lattices is obtained. As a direct application, a complete criterion of a weak convergence of sequences in l infinity is formulated.
The class of Banach spaces, which do not have c0 as a spreading model, is not L2-hereditary
The classical subspaces of the projective tensor products of and C(α) spaces, α < ω₁
We completely determine the and C(K) spaces which are isomorphic to a subspace of , the projective tensor product of the classical space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states that the only...
The cofinal property of the reflexive indecomposable Banach spaces
It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably -saturated space with and of a saturated space.
The commutators of analysis and interpolation
The boundedness properties of commutators for operators are of central importance in Mathematical Analysis, and some of these commutators arise in a natural way from interpolation theory. Our aim is to present a general abstract method to prove the boundedness of the commutator for linear operators and certain unbounded operators that appear in interpolation theory, previously known and a priori unrelated for both real and complex interpolation methods, and also to show how the abstract result...
The Compact Approximation Property does not imply the Approximation Property
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
The compact endomorphisms of the metric linear spaces