Quasi-ordered Desarguesian affine spaces

Starting from Euclidean spaces with a betweenness function, which is compatible with the congruence relation, we introduce quasi-orderings as a common generalization of half-orderings and semi-orderings. Quasi-ordered Desarguesian affine spaces are described algebraically by guasi-ordered skew fields.Dedicated to Professor Dr. W. Benz on the occasion of his 60 th birthday     

Locally FCC spaces

We introduce the class of locally FCC spaces, study various properties of such spaces and investigate their relationships with some other related spaces. This revised version was published online in June 2006 with corrections to the Cover Date.     

Locally flat Banach spaces

The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher order smoothness is involved. In this note we investigate the structural properties of Banach spaces admitting (arbitrary) bump functions depending locally on finitely many coordinates. This work was supported by the research project MSM 0021620839 and by the grant of the Grant Agency of the Czech Republic No. 201/05/P582 and No. 201/06/0018.     

Locally conformally homogeneous pseudo-Riemannian spaces

Locally homogeneous Riemannian spaces were studied in [1–4]. Locally conformally homogeneous Riemannian spaces were considered in [10]. Moreover, the theorem claiming that every such space is either conformally flat or conformally equivalent to a locally homogeneous Riemannian space was proved.In this article, we study locally conformally homogeneous pseudo-Riemannian spaces and prove a theorem on their structure. Using three-dimensional Lie groups and the six-dimensional Heisenberg group [11], we construct some examples showing the difference between the Riemannian and pseudo-Riemannian cases for such spaces.     

Locally symmetric positively curved Finsler spaces

We showed that any compact locally symmetric Finsler metric with positive flag curvature must be Riemannian. Dedicated to Professor Karsten Grove on the occassion of his sixtieth birthday Received: 8 May 2006     

Desarguesian spreads

We review some constructions related with desarguesian spreads of projective spaces of finite dimension over a skewfield.     

Locally symmetric Finsler spaces in negative curvature

É. Cartan introduced in 1926 the Riemannian locally symmetric spaces, as the spaces whose curvature tensor is parallel. They also owe their name to the fact that, for each point, the geodesic reflexion is a local isometry. The aim of this Note is to announce a strong rigidity result for Finsler spaces. Namely, we show that a negatively curved locally symmetric (in the first sense above) Finsler space is isometric to a Riemann locally symmetric space.     

Locally definite normal operators in Krein spaces

We introduce the spectral points of two-sided positive type of bounded normal operators in Krein spaces. It is shown that a normal operator has a local spectral function on sets which are of two-sided positive type. In addition, we prove that the Riesz–Dunford spectral subspace corresponding to a spectral set which is only of positive type is uniformly positive. The restriction of the operator to this subspace is then normal in a Hilbert space.     

Locally solvable vector fields and Hardy spaces

We characterize the boundary value of homegeneous solutions of planar one-sided locally solvable vector fields with analytic coefficients with the property that the Lp norm of their traces is locally uniformly bounded, 0<p?1. For p≠1/n, , the boundary value must locally belong to the local Hardy space hp(R) of Goldberg while for p=1/n, , the answer calls for a new class of atomic Hardy spaces if the vector field is of infinite type at some boundary point.     

Locally projective spaces which satisfy the Bundle Theorem

We give a complete and short proof of KAHN's Theorem that every locally projective space (M,M) with dim M3 satisfying the Bundle Theorem is embeddable in a projective space. The central tool of KAHN's proof is the fact that (M,M) is locally projective, while we use mainly the Bundle Theorem.Dedicated to Professor Dr. H. Mäurer on the occasion of his sixtieth birthday     

Locally uniformly rotund points in convex-transitive Banach spaces

Almost transitive superreflexive Banach spaces have been considered in [C. Finet, Uniform convexity properties of norms on superreflexive Banach spaces, Israel J. Math. 53 (1986) 81–92], where it is shown that they are uniformly convex and uniformly smooth. We characterize such spaces as those convex transitive Banach spaces satisfying conditions much weaker than that of uniform convexity (for example, that of having a weakly locally uniformly rotund point). We note that, in general, the property of convex transitivity for a Banach space is weaker than that of almost transitivity.     

Locally finite dimensional shift-invariant spaces in

We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space or the fractional Sobolev space , then the superspace can be chosen to be or , respectively.

     

Desarguesian partial parallelisms

This article establishes connections between Desarguesian partial parallelisms of deficiency one in PG(3,q) and translation planes of orderq ⁴ admitting a collineation group isomorphic to SL(2,q) which is generated by Baer collineations.The author is grateful to Professor Alan Prince for helpful conversations with respect to this article and, in particular, with respect to the actual bounds for certain maximal partial spreads.The author is grateful to the referee for helpful comments in the writing of this article.     

Desarguesian nets without ovals

Let Π be the Desarguesian affine plane coordinatized by a division ring D with charD≠2. For n=6 and also for n=7, we prove that Π holds an n-net without an oval if and only if |D|?9.     

Locally covering maps in metric spaces and coincidence points

We study the notion of α-covering map with respect to certain subsets in metric spaces. Generalizing results from [1] we use this notion to give some coincidence theorems for pairs of single-valued and multivalued maps one of which is relatively α-covering while the other satisfies the Lipschitz condition. These assertions extend some classical contraction map principles. We define the notion of α-covering multimap at a point and give conditions under which the covering property of a multimap at each interior point of a set implies that it is covering on the whole set. As applications we consider the solvability of a system of inclusions and the existence of a positive trajectory for a semilinear feedback control system. This paper is dedicated to Professor Felix Browder on the occasion of his jubilee     

Locally linearly independent bases for bivariate polynomial spline spaces

Locally linearly independent bases are constructed for the spaces S ^r _d () of polynomial splines of degree d3r+2 and smoothness r defined on triangulations, as well as for their superspline subspaces.