Characterizations of elements of best approximation in non-Archimedean normed spaces
Characterizations of inner product spaces by strongly convex functions.
Characterizations of inner product spaces through an isosceles trapezoid property
Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.
Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference
We define the radius of the inscribed and circumscribed circumferences in a triangle located in a real normed space and we obtain new characterizations of inner product spaces.
Characterizations of Kurzweil-Henstock-Pettis integrable functions
We prove that several results of Talagrand proved for the Pettis integral also hold for the Kurzweil-Henstock-Pettis integral. In particular the Kurzweil-Henstock-Pettis integrability can be characterized by cores of the functions and by properties of suitable operators defined by integrands.
Characterizations of -predual spaces by centerable subsets
In this note, we prove that a real or complex Banach space is an -predual space if and only if every four-point subset of is centerable. The real case sharpens Rao’s result in [Chebyshev centers and centerable sets, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2593–2598] and the complex case is closely related to the characterizations of -predual spaces by Lima [Complex Banach spaces whose duals are -spaces, Israel J. Math. 24 (1976), no. 1, 59–72].
Characterizations of nearly-openness.
Characterizations of reduced polytopes in finite-dimensional normed spaces.
Characterizations of seminorms given by continuous linear functionals on normed linear spaces and applications to Gel'fand measures.
Characterizations of series in Banach spaces.
Characterizations of some monotonicity properties of a lattice norm in Musielak-Orlicz spaces
Characterizations of spreading models of
Rosenthal in [11] proved that if is a uniformly bounded sequence of real-valued functions which has no pointwise converging subsequence then has a subsequence which is equivalent to the unit basis of in the supremum norm. Kechris and Louveau in [6] classified the pointwise convergent sequences of continuous real-valued functions, which are defined on a compact metric space, by the aid of a countable ordinal index “”. In this paper we prove some local analogues of the above Rosenthal ’s theorem...
Characterizations of the Completely Regular Topological Spaces X for Which C (X) is a Dual Ordered Vector Space.
Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings.
Characterizations of weakly compact sets and new fixed point free maps in c₀
We give a basic sequence characterization of relative weak compactness in c₀ and we construct new examples of closed, bounded, convex subsets of c₀ failing the fixed point property for nonexpansive self-maps. Combining these results, we derive the following characterization of weak compactness for closed, bounded, convex subsets C of c₀: such a C is weakly compact if and only if all of its closed, convex, nonempty subsets have the fixed point property for nonexpansive mappings.
Characterizing algebras of -functions on manifolds
Among all -algebras we characterize those which are algebras of -functions on second countable Hausdorff -manifolds.
Characterizing discrete vector lattices
Characterizing Fréchet-Schwartz spaces via power bounded operators
We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet-Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a Fréchet-Schwartz space does so in a special way. We single out this type of "rapid convergence" for a sequence...
Characterizing Hilbert space topology
Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections
We characterize those anisotropic Sobolev spaces on tori in the and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author’s earlier paper [W].