On linear properties of separable conjugate spaces of C*-algebras
On local and global moduli of convexity
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 locally uniformly convex and differentiable norms in certain non-separable Banach spaces
On mappings, orthogonally additive in the Birkhoff-James sense.
On metric projections and distance functions in Banach spaces
On Milman's moduli for Banach spaces.
On minimal points
On minimal points with respect to a set in Banach spaces
On minimal sequences of type and bounded biorthogonal systems in Banach spaces
On minimality and lp-complemented subspaces of Orlicz function spaces.
Several properties of the class of minimal Orlicz function spaces LF are described. In particular, an explicitly defined class of non-trivial minimal functions is shown, which provides concrete examples of Orlicz spaces without complemented copies of F-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 modular sequence spaces
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 generalizations of the concept of nuclear operators
This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear mapping...
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 multilinear mappings of nuclear type.
The space of multilinear mappings of nuclear type (s;r1,...,rn) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.