Snarked sums of Banach spaces.
Sobczyk's theorems from A to B.
Sobczyk's theorem is usually stated as: every copy of c0 inside a separable Banach space is complemented by a projection with norm at most 2. Nevertheless, our understanding is not complete until we also recall: and c0 is not complemented in l∞. Now the limits of the phenomenon are set: although c0 is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l∞.
Some applications of martingales in Banach spaces
Some Examples Concerning Rotundity in Banach Spaces.
Some permanence results of properties of Banach spaces
Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.
Some properties of ,0 < p < 1
Some remarks on non-separable Banach spaces with Markuševič basis
Some remarks on subspaces of weakly compactly generated Banach spaces
Some remarks on the equality
We show that the equality is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product of two Banach spaces under some approximation property type assumptions.
Some remarks on the Gurarij space
Some strongly bounded classes of Banach spaces
We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach space.
Some version of Gowers' dichotomy for Banach spaces.
Spaces of compact operators on spaces
We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces , the topological products of Cantor cubes and intervals of ordinal numbers [0,α].
Spaces of Lipschitz and Hölder functions and their applications.
We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 < α < 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l∞. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if and only if...
Stability in Banach spaces.
Strong subdifferentiability of norms and geometry of Banach spaces
The strong subdifferentiability of norms (i.eȯne-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.
Subsets of the unit ball the are separated by more than one
Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure
It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.
Sums of SCD sets and their applications to SCD operators and narrow operators
We answer two open questions concerning the recently introduced notions of slicely countably determined (SCD) sets and SCD operators in Banach spaces. An application to narrow operators in spaces with the Daugavet property is given.
Supereflexive Banach spaces