General reflexivity and pattern subspaces

This paper extends the theory of reflexivity triples by extending notions and results in the theory of dual operator algebras to this more general setting. In addition, a complete and simple characterization is given for the reflexivity of two-dimensional pattern spaces of finite matrices.     

Reflexivity with maximal ideal axes

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. We in this note study rings with the reflexivity whose axis is given by maximal ideals (simply, an RM ring) which are a generalization of symmetric rings. It is first shown that the reflexivity of a ring and the RM ring property are independent of each other, noting that both of them are generalizations of ideal-symmetric rings. We connect RM rings with reflexive rings in various situations raised naturally in the procedure. As a generalization of RM rings, we also study the structure of the reflexivity with the maximal ideal axis on idempotents (simply, an RMI ring) and then investigate the structure of minimal non-Abelian RMI rings (with or without identity) up to isomorphism.     

James sequences and Dependent Choices

We prove James's sequential characterization of (compact) reflexivity in set‐theory ZF + DC , where DC is the axiom of Dependent Choices. In turn, James's criterion implies that every infinite set is Dedekind‐infinite, whence it is not provable in ZF . Our proof in ZF + DC of James' criterion leads us to various notions of reflexivity which are equivalent in ZFC but are not equivalent in ZF . We also show that the weak compactness of the closed unit ball of a (simply) reflexive space does not imply the Boolean Prime Ideal theorem : this solves a question raised in [6]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

弱代数性自反与强代数性自反

Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.     

A preliminary model of participation for small groups

We present a small-group model that moderates agent behavior using several factors to illustrate the influence of social reflexivity on individual behavior. To motivate this work, we review a validated simulation of the Battle of Medenine. Individuals in the battle performed with greater variance than the simulation predicted, suggesting that individual differences are important. Using a light-weight simulation, we implement one means of representing these differences inspired in part by Grossman’s (On Killing: The Psychological Cost of Learning to Kill in War and Society. Little, Brown and Company, New York, 1995) participation formula. This work contributes to a general theory of social reflexivity by offering a theory of participation as a social phenomenon, independent of explicit agent knowledge. We demonstrate that our preliminary version of the participation model generates individual differences that in turn have a meaningful impact on group performance. Specifically, our results suggest that a group member’s location with respect to other group members and observers can be an important exogenous source of individual differences.     

CONSTRAINED CONTROLLABILITY IN NON REFLEXIVE BANACH SPACES

Abstract

Throughout the literature on optimal control in Banach spaces, hypotheses like “separable and reflexive” are frequently encountered. In this note we consider one such case, studied by Peichl and Schappacher. Using techniques from Banach space theory and the theory of vector measures, we show how to remove the hypothesis of reflexivity and translate the problem of controls to one about the strong continuity of an adjoint semigroup on the positive real axis.     

Lifting of the approximation property from Banach spaces to their dual spaces

Inspired by the principle of local reflexivity, due to Lindenstrauss and Rosenthal, a new geometric property of Banach spaces, the extendable local reflexivity, was recently introduced by Rosenthal. Johnson and Oikhberg proved that the extendable local reflexivity permits lifting the bounded approximation property from Banach spaces to their dual spaces. It is not known whether the extendable local reflexivity permits lifting the approximation property. We prove that it does whenever the space is complemented in its bidual. This involves the concept of the weak bounded approximation property, introduced by Lima and Oja.

     

算子子空间的渐近自反性和遗传性

研究了算子子空间的渐近自反性问题，渐近自反子空间的遗传斯近自反性以及某些单个算子的渐近自反性．我们也讨论了投影网类的浙近自反性。     

The James theorem in complete random normed modules

The purpose of this paper is to generalize the classical James theorem characterizing the reflexivity of Banach spaces to one characterizing the random reflexivity of complete random normed modules.     

Bounded Reflexivity of Operator Spaces

We introduce a concept bounded reflexivity for a subspace of operators on a normed space. We explore the properties of bounded reflexivity, study the similarities and differences between bounded reflexivity and the usual reflexivity for a subspace of operators. As applications of bounded reflexivity, we give alternative proofs of some well known results about positivity and complete positivity of elementary operators.     

关于(余)反射的等价性和可扩张性及其应用

该文研究了（余）反射的等价性和可扩张性及应用，得到的主要结果如下：(1) 余反射余代数范畴和反射代数范畴是等价的．(2) 反射和余反射都具有可扩张性．使用这些结果可以用来推广和化简［1-4］中部分结论     

Principle of local reflexivity respecting subspaces

We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting of a Banach space and its subspace.     

The separability of the Gauss map versus the reflexivity

In projective algebraic geometry, various pathological phenomena in positive characteristic have been observed by several authors. Many of those phenomena concerning the behavior of embedded tangent spaces seem to be controlled by the separability of (the extension of function fields defined by) the Gauss map, or by the reflexivity with respect to the projective dual for a projective variety. The purpose of this paper is to survey the studies on the relationship between the separability of the Gauss map and the reflexivity for a projective variety: Is the separability of the Gauss map equivalent to the reflexivity for a projective variety?     

Reflexivity of bilattices

We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice ? we may associate a bilattice Σ_?. Similarly, having a bilattice Σ we may construct a subspace lattice Σ_?. Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.     

Ehrhart Series,Unimodality, and Integrally Closed Reflexive Polytopes

An interesting open problem in Ehrhart theory is to classify those lattice polytopes having a unimodal h*-vector. Although various sufficient conditions have been found, necessary conditions remain a challenge. In this paper, we consider integrally closed reflexive simplices and discuss an operation that preserves reflexivity, integral closure, and unimodality of the h*-vector, providing one explanation for why unimodality occurs in this setting. We also discuss the failure of proving unimodality in this setting using weak Lefschetz elements.     

Réflexivité d’une extension d’un opérateur normal par un opérateur nilpotent

Let T be an extension of a one to one normal operator A by a nilpotent operator N. In this paper we calculate the defect of reflexivity of T. We give a necessary and sufficient condition to insure the reflexivity of such extensions. In particular, it is shown that T is reflexive when N is reflexive.     

自反和超自反子空间格

本文讨论了子空间格的序和、序积的自反和超自反性以及它们对应的代数的超自反性。     

An elementary proof of the principle of local reflexivity

We give an elementary proof of the principle of local reflexivity.

     

Reflexivity of Powers of the Multiplication Operator on Special Function Spaces

In this paper we present sufficient conditions for reflexivity of any powers of the multiplication operator acting on Banach spaces of formal Laurent series.     

Duality of Besov,Triebel–Lizorkin and Herz spaces with variable exponents

Our aim is to prove duality and reflexivity of Besov spaces, Triebel–Lizorkin spaces and Herz spaces with variable exponents.