Positive Semicharacters of Lie Semigroups

We study positive semicharacters of generating Lie subsemigroup of a connected Lie group . These semicharacters are important for positive representations of in Hilbert space and for completely monotonic functions in . We describe the tangent map for a positive semicharacter and then obtain a necessary and sufficient condition for nontriviality of the wedge consisting of all bounded positive semicharacters of . In particular is nontrivial for a solvable simply connected and invariant without nontrivial subgroups, but it is trivial for a semisimple .     

Commutativity of the Arens product in lattice ordered algebras

Let be an Abelian Archimedean lattice ordered algebra. The order bidual furnished with the Arens product is again a lattice ordered algebra. We show that the order continuous order bidual is Abelian. This solves an open problem and improves a result of Scheffold, who proved it for the case of normed lattice ordered algebras. The proof is based on the up-down-up approximation of positive elements in the order continuous order bidual by elements in the canonical image of in Components of positive elements in are characterized and the result is applied to the Arens product of -and almost -algebras.     

Convex Subgroups of Partially Right-Ordered Groups

We study into the question of whether a partial order can be induced from a partially right-ordered group onto a space of right cosets of w.r.t. some subgroup of . Examples are constructed showing that the condition of being convex for in is insufficient for this. A necessary and sufficient condition (in terms of a subgroup and a positive cone of ) is specified under which an order of can be induced onto . Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups for which is partially ordered for every convex subgroup , and properties of the class of groups such that is partially ordered for every partial right order on and every subgroup that is convex under .     

Application of Upper Hemi-Continuous Operators on Generalized Bi-quasi-variational Inequalities in Locally Convex Topological Vector Spaces

Let and be Hausdorff topological vector spaces over the field , let be a bilinear functional, and let be a non-empty subset of . Given a set-valued map and two set-valued maps , the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point and a point such that and for all and for all or to find a point a point and a point such that and for all . The generalized bi-quasi-variational inequality was introduced first by Shih and Tan [8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators [4] in locally convex topological vector spaces on compact sets.     

Superlocals in Symmetric and Alternating Groups

On Aschbacher's definition, a subgroup N of a finite group is called a -superlocal for a prime if . We describe the -superlocals in symmetric and alternating groups, thereby resolving part way Problem 11.3 in the Kourovka Notebook [3].     

Orbits of Positive Operators from a Differentiable Viewpoint

Let be a unital C^*-algebra and G the group of units of . A geometrical study of the action of G over the set ⁺ of all positive elements of is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in 'components' which also have a rich geometrical structure.     

A Short Solution to the Busemann-Petty Problem

A unified analytic solution to the Busemann-Petty problem was recently found by Gardner, Koldobsky and Schlumprecht. We give an elementary proof of their formulas for the inverse Radon transform of the radial function of an origin-symmetric star body .     

Almost periodic compactifications of group extensions

Let and be groups and let be an extension of by . Given a property of group compactifications, one can ask whether there exist compactifications and of N and K such that the universal -compactification of G is canonically isomorphic to an extension of by . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties and then apply this result to the almost periodic and weakly almost periodic compactifications of G.     

Lp Contraction Semigroups for Vector Valued Functions

Let be a contraction semigroup on the space of vector valued functions ( is a Hilbert space). In order to study the extension of to a contaction semigroup on , Shigekawa [Sh] studied recently the domination property where is a symmetric sub-Markovian semigroup on . He gives in the setting of square field operators sufficient conditions for the above inequality. The aim of the present paper is to show that the methods of [12] and [13] can be applied in the present setting and provide two ways for the extension of to We give necessary and sufficient conditions in terms of sesquilinear forms for the contractivity property as well as for the above domination property in a more general situation.     

Precovers

Let be an abstract class (closed under isomorpic copies) of left R-modules. In the first part of the paper some sufficient conditions under which is a precover class are given. The next section studies the -precovers which are -covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left R-modules. Especially, several sufficient conditions for the existence of -torsionfree and -torsionfree -injective covers are presented.     

Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line

Let be a field of formal power series with real coefficients, whose supports are well ordered subsets of an Abelian group of cardinality strictly less than . For , we give criteria of a section being symmetric and of a symmetric section being Dedekind. It is proved that an -saturated non-standard real line is isomorphic to some field of the form . For , some consequences are inferred regarding symmetric sections, and the cofinality of banks of the sections.     

Basic subgroups in abelian group rings

Suppose is a commutative ring with identity of prime characteristic and is an arbitrary abelian -group. In the present paper, a basic subgroup and a lower basic subgroup of the -component and of the factor-group of the unit group in the modular group algebra are established, in the case when is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed -component and of the quotient group are given when is perfect and is arbitrary whose is -divisible. These results extend and generalize a result due to Nachev (1996) published in Houston J. Math., when the ring is perfect and is -primary. Some other applications in this direction are also obtained for the direct factor problem and for a kind of an arbitrary basic subgroup.     

Frobenius Groups Generated by Quadratic Elements

An automorphism of a group X is said to be quadratic if there exist integers and such that for any . If is a Frobenius group then an element is said to be quadratic if induces, by conjugation in the core of , a quadratic automorphism. By definition, a group H acts on a group F freely if for and only with or . It is proved that a Frobenius group generated by two quadratic elements is finite and its core is commutative. In particular, any Frobenius group generated by two elements of order at most 4 is finite. Also we argue that a Frobenius group with finitely generated soluble core is finite. The results mentioned are used to show that a group acting freely on an Abelian group is finite if it is generated by elements of order 3, and the order of a product of every two elements of order 3 in is finite.     

Conservativeness and Extensions of Feller Semigroups

Let denote a Feller semigroup on , and itsextension to the bounded measurable functions. We show that . If the generator of the semigroup is a pseudo-differential operator we can restate this condition in terms of the symbol. As a by-product, we obtain necessary and sufficient conditions for the conservativeness of the semigroup which are again expressed through the symbol.     

Direct Theorem about Approximation on a Family of Two Segments

Introduce the notation: , is the union of two segments [-1,1] and [-1 + ,1+ ], is a noninteger number, is the Hölder class with exponent on The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a ₁ ( ) , b ₁ ( ) 0 depending only on such that for any there exists a polynomial , such that . Bibliography: 11 titles.     

On a Problem of the Theory of Multiply Local Formations

We describe the -closed n-multiply local formations such that the lattice of all -closed n-multiply local formations between and is Boolean.     

Determinants in Triangulated Categories

For a small triangulated category , Bass's K ₁ group is described, and the theorem of the heart is proved. We define the determinant map from to Neeman's , and we compute this map when is the derived category of an Abelian category .     

On a certain Maximum Principle for Positive Operators in an Ordered Normed Space

The equation for a positive linear continuous operator is considered in an ordered normed space , where the cone is assumed to be closed and having a nonempty interior. Then the dual cone of K possesses a base . Generalizing the well known maximum principle for positive matrices an operator A is said to satisfy the maximum principle, if for any there exists a positive linear continuous functional which is both, maximal on the element Ax, i.e. , and positive on the element x, i.e. 0$$ " align="middle" border="0"> . This property is studied and characterized both analytically by some extreme point condition and geometrically by means of the behaviour under A of the faces of the cone K. It is shown that the conditions which have been obtained for finite dimensional spaces in earlier relevant papers are special cases of conditions presented in this paper. The maximum pinciple is proved for simple operators in the spaces and c.