Topologically left invariant means on semigroup algebras

LetM(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroupS with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions forM(S)* to have a topologically left invariant mean.     

Diagonal Invariant Ideals of Topologically Graded C*-algebras

We study diagonal invariant ideals of topologically graded C~*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.     

SOME TOPOLOGICAL PROPERTIES OF ENDOMORPHISMS OF THE UNIT CIRCLE

In this paper, we give a simple proof for some topological properties of endomorphisms on the unit circle.     

On the Space of Weakly Almost Periodic Functionals and Its Amenability

Let S be a locally compact semitopological semigroup with measure algebra M(S), M₀(S) the set of all probability measures in M(S) and WF(S) the space of weakly almost periodic functionals on M(S)^*. Assuming that M₀(S) has the semiright invariant isometry property, it is shown that WF(S) has a topological left invariant mean (TLIM) whenever the center of M₀(S) is nonempty; in particular if either the center of S is nonempty or S has a left identity, then WF(S) has a TLIM. Finally if, for each M₀(S), the mapping v v * of M₀(S) into itself is surjective and the center of M₀(S) is nonempty, then WF(S) has a TLIM. We also generalize some results from discrete case to topological one.AMS Subject Classification (1991): 43A07     

Recent Progress in Polyhedral Harmonics

Polyhedral harmonics is a subject which deals with the problem of characterizing the continuous functions satisfying the mean value property with respect to a polytope. The main feature of it is the finite dimensionality of the space of polyhedral harmonic functions. The theory involves not only analysis but also algebra and combinatorics, and has a rather different flavor from classical harmonic analysis. This paper aims at providing a survey on the subject, focusing on the author's recent results.     

关于C(Ω)中可补子空间的一个注记

本文将指出：对于连续函数空间C（Ω）而言（其中，Ω为某紧度空间），其内任一“（格）理想”必为其（拓扑）可补子空间．     

Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Norm inequalities for matrix geometric means of positive definite matrices

We obtain eigenvalue inequalities for matrix geometric means of positive definite matrices. This implies matrix norm inequalities for unitarily invariant norms, which are considered as complementary to a series of norm inequalities among geometric means. We give complements of the Ando–Hiai type inequality for the Karcher mean by means of the generalized Kantorovich constant. Finally, we consider the monotonicity of the eigenvalue function for the Karcher mean.     

Norm inequalities in operator ideals

In this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm. Among the well-known inequalities which can be proved with this technique are the Löwner-Heinz inequality, inequalities relating various operator means and the Corach-Porta-Recht inequality. We prove two general inequalities and from them we derive several inequalities by specialization, many of them new. We also show how some inequalities, known to be valid for matrices or bounded operators, can be extended with this technique to normed ideals in C^∗-algebras, in particular to the noncommutative Lp-spaces of a semi-finite von Neumann algebra.     

A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS

For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.     

Weak amenability components ofL 1(G)-modules, amenable groups, and an ergodic theorem

Weak versions of amenability components of BanachL ₁(G)-modules are considered. Using these versions, a mean ergodic theorem for locally compact groups is formulated. The possibility of using weak amenability components of operatorL ₁(G)-modules to characterize ameable groups is studied. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 879–886, December, 1999.     

Topologically Irreducible Representations and Radicals in Banach Algebras

It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of ‘topologicalradicals’ in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx.     

Convergence of almost-orbits of nonexpansive semigroups in Banach spaces

The purpose of this paper is to show that the study of mean ergodic theorems for almost-orbits of semigroups of nonexpansive mappings on closed convex subsets of a Banach space can be reduced to the study of orbits for semigroups of nonexpansive mappings. This provides a unified approach to various mean ergodic theorems for almost-orbits in the literature and new applications.

     

Clean elements in abelian rings

Let R be a ring with identity. An element in R is said to be clean if it is the sum of a unit and an idempotent. R is said to be clean if all of its elements are clean. If every idempotent in R is central, then R is said to be abelian. In this paper we obtain some conditions equivalent to being clean in an abelian ring.     

Invariant surfaces in the homogeneous space Sol with constant curvature

A surface in homogeneous space is said to be an invariant surface if it is invariant under some of the two 1‐parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curvature. Also, we characterize invariant surfaces that satisfy a linear Weingarten relation.