Some results on norm attaining bilinear forms on L1[0,1].
We characterize the norm attaining bilinear forms on L1[0,1], and show that the set of norm attaining ones is not dense in the space of continuous bilinear forms on L1[0,1].
Some results on packing in Orlicz sequence spaces
We present monotonicity theorems for index functions of N-fuctions, and obtain formulas for exact values of packing constants. In particular, we show that the Orlicz sequence space generated by the N-function N(v) = (1+|v|)ln(1+|v|) - |v| with Luxemburg norm has the Kottman constant , which answers M. M. Rao and Z. D. Ren’s [8] problem.
Some results on symmetric subspaces of
Some Structures Related to Metric Projections in Orlicz Spaces
We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.
Some translation-invariant Banach function spaces which contain c₀
We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space c₀.
Sous-Différentiabilité de fonctions convexes à valeurs dans un espace vectoriel ordonné.
Sous-espaces complémentés de
Sous-espaces complémentés de , d’ après P. Enflo
Space of Baire functions. I
Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of -analytic spaces, called disjoint analytic spaces, and on all pseudocompact spaces. The sequential stability index for the Banach space of bounded continuous real-valued functions on these spaces is shown to be either , or (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces with index...
Spaces defined by the level function and their duals
The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of . These domains are shown to be Banach spaces which, although closely tied to spaces, are not reflexive. A related construction is given which characterizes their dual spaces.
Spaces of measurable functions
For a metrizable space X and a finite measure space (Ω, , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.
Spaces of Vector-Valued Measurable Functions.
Spectral properties of Schrödinger operators and scattering theory
Stable points of unit ball in Orlicz spaces
The aim of this paper is to investigate stability of unit ball in Orlicz spaces, endowed with the Luxemburg norm, from the “local” point of view. Firstly, those points of the unit ball are characterized which are stable, i.e., at which the map is lower-semicontinuous. Then the main theorem is established: An Orlicz space has stable unit ball if and only if either is finite dimensional or it is isometric to or satisfies the condition or (appropriate to the measure and the function...
Strictly and uniformly monotone sequential Musielak-Orlicz spaces.
Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces
If G is the closure of in exp L₂, it is proved that the inclusion between rearrangement invariant spaces E ⊂ F is strictly singular if and only if it is disjointly strictly singular and E ⊊ G. For any Marcinkiewicz space M(φ) ⊂ G such that M(φ) is not an interpolation space between and G it is proved that there exists another Marcinkiewicz space M(ψ) ⊊ M(φ) with the property that the M(ψ) and M(φ) norms are equivalent on the Rademacher subspace. Applications are given and a question of Milman...
Strong barrelledness properties in L...(..., X).
Strong barrelledness properties in Lebesgue-Bochner spaces.
Strong extrapolation spaces and interpolation.
Strong law of large numbers for optimal points.