On -nearly uniform convex property in generalized Cesàro sequence spaces.
On K-nearly uniform convexity in Orlicz spaces.
On Kottman's constants in Banach spaces
This paper deals with a few, not widely known, aspects of Kottman's constant of a Banach space and its symmetric and finite variations. We will consider their behaviour under ultrapowers, relations with other parameters such as Whitley's or James' constant, and connection with the extension of c₀-valued Lipschitz maps.
On large subspaces of the Schatten -classes
On local convexity of nonlinear mappings between Banach spaces
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.
On mappings, orthogonally additive in the Birkhoff-James sense.
On Milman's moduli for Banach spaces.
On minimal points
On minimal points with respect to a set in Banach spaces
On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions
We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.
On moduli of convexity in Banach spaces.
On moduli of expansion of the duality mapping of smooth Banach spaces.
On moduli of -convexity.
On monotonic functions from the unit interval into a Banach space with uncountable sets of points of discontinuity
We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. We show that if f: [0,1] → X is an increasing function with respect to a norming subset E of X* with uncountably many points of discontinuity and Q is a countable dense subset of [0,1], then (1) contains an order isomorphic copy of D(0,1), (2) contains an isomorphic copy of C([0,1]), (3) contains an isomorphic copy of c₀(Γ) for some uncountable set Γ, (4) if...
On multilinear mappings attaining their norms.
We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.
On -normed spaces.
On nearly euclidean decomposition for some classes of Banach spaces
On nested sequences of convex sets in Banach spaces
We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.
On nicely smooth Banach spaces.
On non-midpoint locally uniformly rotund normability in Banach spaces.