On one generalization of weakly compactly generated Banach spaces
On operators fixing copies of and
On operators from separable reflexive spaces with asymptotic structure
Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower--tree estimate and let T be a bounded linear operator from X which satisfies an upper--tree estimate. Then T factors through a subspace of , where (Fₙ) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an FDD. Similarly, let 1 < q < r < p < ∞ and let X be a separable reflexive Banach space satisfying an asymptotic lower--tree...
On operators that preserve the Radon-Nikodým property.
On operators which factor through or c₀
Let 1 < p < ∞. Let X be a subspace of a space Z with a shrinking F.D.D. (Eₙ) which satisfies a block lower-p estimate. Then any bounded linear operator T from X which satisfies an upper-(C,p)-tree estimate factors through a subspace of , where (Fₙ) is a blocking of (Eₙ). In particular, we prove that an operator from (2 < p < ∞) satisfies an upper-(C,p)-tree estimate if and only if it factors through . This gives an answer to a question of W. B. Johnson. We also prove that if X is...
On order structure and operators in L ∞(μ)
It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.
On - and -convexity of Banach spaces.
On -convex Musielak-Orlicz spaces
In this paper there is proved that every Musielak-Orlicz space is reflexive iff it is -convex. This is an essential extension of the results given by Ye Yining, He Miaohong and Ryszard Płuciennik [16].
On p-absolutely summing operators acting on Banach lattices
On pairs of Banach spaces which are isomorphic to complemented subspaces of each other
We establish the existence of Banach spaces E and F isomorphic to complemented subspaces of each other but with isomorphic to , m, n, p, q ∈ ℕ, if and only if m = p and n = q.
On Pelczynski's property (V*) in vector sequence spaces.
On perfectly homogeneous bases in quasi-Banach spaces.
On Polish spaces Lipschitz universal for separable metric spaces
On polynomial equations in Banach space, perturbation techniques and applications.
On positive embeddings of C(K) spaces
We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such as countable...
On positive operator-valued continuous maps
In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that
On prequojections and their duals.
The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce a special class...
On Primary Simplex Spaces.
On probabilistic normed spaces under .
On projectional skeletons in Vašák spaces
We provide an alternative proof of the theorem saying that any Vašák (or, weakly countably determined) Banach space admits a full -projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W. Kubiś (2009) in case of weakly compactly generated spaces.