On vector-valued analytic functions with constant norm
On WCG Banach spaces with norms which are uniformly differentiable in every direction
On weak drop property and quasi-weak drop property
Every weakly sequentially compact convex set in a locally convex space has the weak drop property and every weakly compact convex set has the quasi-weak drop property. An example shows that the quasi-weak drop property is strictly weaker than the weak drop property for closed bounded convex sets in locally convex spaces (even when the spaces are quasi-complete). For closed bounded convex subsets of quasi-complete locally convex spaces, the quasi-weak drop property is equivalent to weak compactness....
On weak (r,2)-summing operators and weak Hilbert spaces
On weak sequential convergence in JB*-triple duals
We study various Banach space properties of the dual space E* of a homogeneous Banach space (alias, a JB*-triple) E. For example, if all primitive M-ideals of E are maximal, we show that E* has the Alternative Dunford-Pettis property (respectively, the Kadec-Klee property) if and only if all biholomorphic automorphisms of the open unit ball of E are sequentially weakly continuous (respectively, weakly continuous). Those E for which E* has the weak* Kadec-Klee property are characterised by a compactness...
On weak statistical convergence.
On weakly extremal structures in Banach spaces.
On weakly locally uniformly rotund norms which are not locally uniformly rotund
We show that every infinite-dimensional Banach space with separable dual admits an equivalent norm which is weakly locally uniformly rotund but not locally uniformly rotund.
On weakly uniformly convex spaces according to Calder.
On weakly uniformly rotund spaces
On weighted James' spaces.
In this note we study the topological structure of weighted James spaces J(h). In particular we prove that J(h) is isomorphic to J if and only if the weight h is bounded. We also provide a description of J(h) if the weight is a non-decreasing sequence.
On weighted Ostrowski type inequalities for operators and vector-valued functions.
On W*UR point and UR point of Orlicz spaces with Orlicz norm.
For Orlicz spaces with Orlicz norm, a criterion of W*UR point is given, and previous results about UR points and WUR points are amended.
On -Chebyshev subspaces of Banach spaces.
On -porous sets in abstract spaces.
On τδ-completeness of H(U).
On ω*-basic sequences and their applications to the study of Banach spaces
Once more on continuity of maximal monotone mappings
Once more on positive commutators
Let A and B be bounded operators on a Banach lattice E such that the commutator C = AB - BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This answers an open question posed by Bračič et al. [Positivity 14 (2010)], where the study of positive commutators of positive operators was initiated.
Ondelettes et bases hilbertiennes.