Tensor Sequences and Inductive Limits with Local Partition of Unity.
The almost lattice isometric copies of in Banach lattices
In this paper it is shown that if a Banach lattice contains a copy of , then it contains an almost lattice isometric copy of . The above result is a lattice version of the well-known result of James concerning the almost isometric copies of in Banach spaces.
The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces
Following Banakh and Gabriyelyan (2016) we say that a Tychonoff space X is an Ascoli space if every compact subset of is evenly continuous; this notion is closely related to the classical Ascoli theorem. Every -space, hence any k-space, is Ascoli. Let X be a metrizable space. We prove that the space is Ascoli iff is a -space iff X is locally compact. Moreover, endowed with the weak topology is Ascoli iff X is countable and discrete. Using some basic concepts from probability theory and...
The Banach space c0.
The Banach space H...(X, d, ...).I.
The Banach space H...(X, d, ...).II.
The Banach Spaces ...p(n) for large p and n.
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 complemented subspace problem revisited
We show that if X is an infinite-dimensional Banach space in which every finite-dimensional subspace is λ-complemented with λ ≤ 2 then X is (1 + C√(λ-1))-isomorphic to a Hilbert space, where C is an absolute constant; this estimate (up to the constant C) is best possible. This answers a question of Kadets and Mityagin from 1973. We also investigate the finite-dimensional versions of the theorem.
The criteria for local uniform rotundity of Orlicz spaces
The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices
The dual of the James tree space is asymptotically uniformly convex
The dual of the James tree space is asymptotically uniformly convex.
The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces
The Dunford-Pettis property, the Gelfand-Phillips property, and L-sets
The Dunford-Pettis property and the Gelfand-Phillips property are studied in the context of spaces of operators. The idea of L-sets is used to give a dual characterization of the Dunford-Pettis property.
The Embeddability of c₀ in Spaces of Operators
Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space , as well as the complementation of the space of w*-w compact operators in the space of w*-w operators from X* to Y.
The fixed point property in a Banach space isomorphic to
We consider a Banach space, which comes naturally from and it appears in the literature, and we prove that this space has the fixed point property for non-expansive mappings defined on weakly compact, convex sets.
The functor σ²X
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.
The geometry of -spaces over atomless measure spaces and the Daugavet property.
The inclusion theorem for multiple summing operators
We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.