Rings of quasi-endomorphisms of strongly indecomposable torsion-free Abelian groups

In the paper the classification of rings of quasi-endomorphisms of strongly indecomposable Abelian torsion-free groups of rank three is obtained. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 763–773, May, 1998.     

完全广义混合强非线性变分包含的解的灵敏性分析

引入并研究了Hilbert空间中一类新的完全广义混合强非线性变分包含．利用改进的隐预解算子技巧分析了此变分包含的解的灵敏性，所得结果改进并推广了以往相应结果．     

On completely hyperexpansive operators

We introduce and discuss a class of operators, to be referred to as the class of completely hyperexpansive operators, which is in some sense antithetical to the class of contractive subnormals. The new class is intimately related to the theory of negative definite functions on abelian semigroups. The known interplay between positive and negative definite functions from the theory of harmonic analysis on semigroups can be exploited to reveal some interesting connections between subnormals and completely hyperexpansive operators.

     

Tilings,packings, coverings,and the approximation of functions

A packing (resp. covering) ? of a normed space X consisting of unit balls is called completely saturated (resp. completely reduced) if no finite set of its members can be replaced by a more numerous (resp. less numerous) set of unit balls of X without losing the packing property (resp. covering property) of ?. We show that a normed space X admits completely saturated packings with disjoint closed unit balls as well as completely reduced coverings with open unit balls, provided that there exists a tiling of X with unit balls. Completely reduced coverings by open balls are of interest in the context of an approximation theory for continuous real‐valued functions that rests on so‐called controllable coverings of compact metric spaces. The close relation between controllable coverings and completely reduced coverings allows an extension of the approximation theory to non‐compact spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Completely positive module maps and completely positive extreme maps

Let be unital -algebras and be the set of all completely positive linear maps of into . In this article we characterize the extreme elements in , for all , and pure elements in in terms of a self-dual Hilbert module structure induced by each in . Let be the subset of consisting of -module maps for a von Neumann algebra . We characterize normal elements in to be extreme. Results here generalize various earlier results by Choi, Paschke and Lin.

     

A theorem of the Dore-Venni type for noncommuting operators

A theorem of the Dore-Venni type for the sum of two closed linear operators is proved, where the operators are noncommuting but instead satisfy a certain commutator condition. This result is then applied to obtain optimal regularity results for parabolic evolution equations and evolutionary integral equations which are nonautonomous. The domains of the involved operators may depend on , but is required to satisfy a certain smoothness property. The results are then applied to parabolic partial differential and integro-differential equations.

     

Noncommutative Geometry and Integrable Models

A construction of conservation laws for -models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing theordinary calculus of differential forms with other differentialcalculi and introducing an analogue of the Hodge operator on thelatter. The general method is illustrated with several examples.     

Hoeffding's inequalities: A counterexample

A sequence : ₀ satisfiesHoeffding's inequality of order n if wheneverX ₁,...,X _n are independent nonnegative integer-valued elementary random variables and are independent identically distributed nonnegative integer-valued elementary random variables, the common distribution of which is the average of those ofX ₁,...,X _n. We show that for each integerm greater than 2 there exists a sequence satisfying Hoeffding's inequality of every order greater thanm but not that of orderm. This answers a question raised by Berg, Christensen, and Ressel.     

The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators

This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.     

On completely multiplicative functions whose values are roots of unity

Summary We prove that if a complex valued completely multiplicative function F and a positive integer ℓ≦5 satisfy the condition F(N) = U_ℓ, where U_ℓ is the set of all ℓ-th roots of unity, then {F(n+1) F(n) ∣ nε N} = U_ℓ.