a bounded approximation of weakly compact operators abstract we study bounded approximation properties of operators it is shown that for every weakly compact operator t on a banach space x if t is uniformly approximated on each compact subset of x by finite rank operators then t 2 can be approximated in the same topology by finite rank operators with the operator norm less than or equal to t 2

the johnson schechtman space has the 6 bounded approximation property abstract in 2001 g godefroy proved that a subspace x js of c 0 constructed by w b johnson and g schechtman in 1996 has the bounded approximation property with 8 this paper slightly improves godefroy s proof establishing that 6

avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation multidimensional unfolding methods suffer from the degeneracy problem in almost all circumstances most degeneracies are easily recognized the solutions are perfect but trivial characterized by approximately equal distances between points from different sets a definition of an absolutely degenerate solution is proposed which makes clear that these solutions only occur when an intercept is present in the transformation function many solutions for the degeneracy problem have been proposed and tested but with little success so far in this paper we offer a substantial modification of an approach initiated bythat introduced a normalization factor based on thevariance in the usual least squares loss function heiser unpublishedthesis 1981 and showed that the normalization factor proposed by kruskal and carroll was not strong enough to avoid degeneracies the factor proposed in the present paper based on the coefficient of variation discourages or penalizes nonmetric transformations of the proximities with small variation so that the procedure steers away from solutions with small variation in the interpoint distances an algorithm is described for minimizing the re adjusted loss function based on iterative majorization the results of a simulation study are discussed in which the optimal range of the penalty parameters is determined two empirical data sets are analyzed by our method clearly showing the benefits of the proposed loss function

integral mappings and the principle of local reflexivity for noncommutative l 1 spaces the operator space analogue of the strong form of the principle of local re exivity is shown to hold for any von neumann algebra predual and thus for any c algebraic dual this is in striking contrast to the situation for c algebras since for example k h does not have that property the proof uses the kaplansky density theorem together with a careful analysis of two notions of integrality for mappings of operator spaces

on subalgebras of the car algebra abstract every nuclear unital separable c algebra a is unitally and completely isometrically ismorphic to the range of a unital completely positive projection on the car algbra b m 2 m 2 let c be a nuclearly imbeddable separable unital c algebra in the sense of voiculescu vo13 then there exists a c subalgebra e of the car algebra b such that c is isomorphic to a quotient c algebra of e we include one of the possible proofs that exact c algebras are nuclearly imbeddable proofs of g covariant analogs are outlined for compact g some related results are obtained on non selfadjoint operator algebras the unital separable nuclear c algebras not of type i are mutually cb isomorphic and have cb distance 256 separable lindenstrauss spaces are isometric to quotients of the car algebra by a sum of closed left and a closed right ideal

multistage ranking models abstract suppose that a sample of people independently examines a fixed set of k items and then ranks these items according to personal judgment the process of ranking the items is decomposed into k 1 stages in the forward model the most preferred item is selected at the first stage the best of the remaining items is selected at the second stage and so on until the least preferred item is selected by default various probability models are adopted at each stage and properties of the resulting models for randomly sampled rankings are investigated luce 1959 first proposed such a modeling scheme where each item i was thought to have an intrinsic value i and the probability of choosing a particular item i at any stage conditional on the set s of items not previously chosen was given by i i s i j s j where i is an indicator function plackett 1975 began with the same model but added interaction terms that would theoretically extend the usefulness of this approach when the basic m

the classification of p compact groups for p odd a p compact group as defined by dwyer and wilkerson is a purely homotopically defined p local analog of a compact lie group it has long been the hope and later the conjecture that these objects should have a classification similar to the classification of compact lie groups in this paper we finish the proof of this conjecture for p an odd prime proving that there is a one to one correspondence between connected p compact groups and finite reflection groups over the p adic integers we do this by providing the last and rather intricate piece namely that the exceptional compact lie groups are uniquely determined as p compact groups by their weyl groups seen as finite reflection groups over the p adic integers our approach in fact gives a largely self contained proof of the entire classification theorem for p odd

stratification and duality for homotopical groups abstract we generalize quillen s f isomorphism theorem quillen s stratification theorem the stable transfer and the finite generation of cohomology rings from finite groups to homotopical groups as a consequence we show that the category of module spectra over c b g f p is stratified and costratified for a large class of p local compact groups g including compact lie groups connected p compact groups and p local finite groups thereby giving a support theoretic classification of all localizing and colocalizing subcategories of this category moreover we prove that p compact groups admit a homotopical form of gorenstein duality

solution of the contractive projection problem in this paper we show that the class of j algebras a class of concrete jordan triple systems is stable under the action of norm one projections this result constitutes a general solution to a problem considered by the authors and others specifically our main result is theorem 2 let p be an arbitrary contractive projection defined on a j algebra m then p m is a jordan triple system in the triple product a b c a b c p f ab c t cb a for a b c e p m and p m has a faithful representation as a j algebra

a recursive partitioning method for the prediction of preference rankings based upon kemeny distances preference rankings usually depend on the characteristics of both the individuals judging a set of objects and the objects being judged this topic has been handled in the literature with log linear representations of the generalized bradley terry model and recently with distance based tree models for rankings a limitation of these approaches is that they only work with full rankings or with a pre specified pattern governing the presence of ties and or they are based on quite strict distributional assumptions to overcome these limitations we propose a new prediction tree method for ranking data that is totally distribution free it combines kemeny s axiomatic approach to define a unique distance between rankings with the cart approach to find a stable prediction tree furthermore our method is not limited by any particular design of the pattern of ties the method is evaluated in an extensive full factorial monte carlo study with a new simulation design

geometric representation of association between categories categories can be counted rated or ranked but they cannot be measured likewise persons or individuals can be counted rated or ranked but they cannot be measured either nevertheless psychology has realized early on that it can take an indirect road to measurement what can be measured is the strength of association between categories in samples or populations and what can be quantitatively compared are counts ratings or rankings made under different circumstances or originating from different persons the strong demand for quantitative analysis of categorical data has thus created a variety of statistical methods with substantial contributions from psychometrics and sociometrics what is the common basis of these methods dealing with categories the basic element they share is that the sample space has a special geometry in which categories or persons are point masses forming a simplex while distributions of counts or profiles of ratings are centers of gravity which are also point masses rankings form a discrete subset in the interior of the simplex known as the permutation polytope and paired comparisons form another subset on the edges of the simplex distances between point masses form the basic tool of analysis the paper gives some history of major concepts which naturally leads to a new concept the shadow point it is then shown how loglinear models luce and rasch models unfolding models correspondence analysis and homogeneity analysis forced classification and classification trees as well as other models and methods fit into this particular geometrical framework

principle of local reflexivity respecting nests of subspaces and the nest approximation properties abstract versions of the principle of local reflexivity which respect given nests of subspaces of a banach space are established as an application some duality and lifting theorems on approximation properties of pairs are extended to the context of nest approximation properties of banach spaces

accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the kemeny axiomatic approach abstract preference rankings virtually appear in all fields of science political sciences behavioral sciences machine learning decision making and so on the well known social choice problem consists in trying to find a reasonable procedure to use the aggregate preferences or rankings expressed by subjects to reach a collective decision this turns out to be equivalent to estimate the consensus central ranking from data and it is known to be a np hard problem a useful solution has been proposed by emond and mason in 2002 through the branch and bound algorithm bb within the kemeny and snell axiomatic framework as a matter of fact bb is a time demanding procedure when the complexity of the problem becomes untractable i e a large number of objects with weak and partial rankings in presence of a low degree of consensus as an alternative we propose an accurate heuristic algorithm called fast that finds at least one of the consensus ranking solutions found by bb saving a lot of computational time in addition we show that the building block of fast is an algorithm called quick that finds already one of the bb solutions so that it can be fruitfully considered to speed up even more the overall searching procedure if the number of objects is low simulation studies and applications on real data allows to show the accuracy and the computational efficiency of our proposal

relative bases in banach spaces abstract we give in this work a new basis definition for banach spaces and investigate some structural properties of certain vector valued function spaces by using it by novelty of the new definition we prove that l has a basis in this sense and so we deduce as a result that it has approximation property in fact we obtain a more general result that the linear subspace p b x of l b x of all those functions with a precompact range has an x schauder basis hence p a x has approximation property if and only if the banach space x has note that p b x l b x for some finite dimensional x further we give a representation theorem to operators on certain vector valued function spaces

lifting convex approximation properties from banach spaces to their dual spaces and the related local reflexivity abstract our main result demonstrates that rather weak forms of the extendable local reflexivity and of the principle of local reflexivity are needed for the lifting of bounded convex approximation properties from banach spaces to their dual spaces this provides a unified approach to the lifting of various bounded approximation properties including besides the classical ones the approximation property for pairs of banach spaces and the positive approximation property of banach lattices

the convex approximation property of banach spaces abstract we study the convex approximation property of banach spaces to provide a unified approach to various approximation properties including besides the classical ones e g the positive approximation property of banach lattices and the approximation property for pairs of banach spaces our main results concern lifting of metric and weak metric approximation properties from banach spaces to their dual spaces as an easy application it follows that if x or x has the radon nikod m property then the approximation property of x defined by a convex subset of conjugate compact operators containing 0 in particular the positive approximation property of x is metric

approaching the rank aggregation problem by local search based metaheuristics abstract encouraged by the success of applying metaheuristics algorithms to other ranking based problems kemeny ranking problem and parameter estimation for mallows distributions in this paper we deal with the rank aggregation problem rap which can be viewed as a generalization of the kemeny problem to arbitrary rankings while in the kemeny problem the input is a set of permutations the rap consists in obtaining the consensus permutation for a sample of arbitrary rankings this is an np hard problem which can be approached by using greedy heuristic algorithms e g borda such algorithms are fast but the solutions so obtained are far to be optimal in this paper we propose the use of more complex search processes to deal with the rap in particular we perform a comparative study among some local based search metaheuristics hill climbing hc iterated local search ils variable neighborhood search vns and greedy randomized adaptive search procedure grasp we provide a complete analysis of the experimental study regarding accuracy and number of iterations required to reach the best solution from the results we can conclude that the selection of a suitable neighborhood plays a key role and that depending on the available resources cpu time a different algorithm vns ils or grasp could be the proper choice

principle of local reflexivity respecting subspaces abstract 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 regression trunk approach to discover treatment covariate interaction the regression trunk approach rta is an integration of regression trees and multiple linear regression analysis in this paper rta is used to discover treatment covariate interactions in the regression of one continuous variable on a treatment variable withmultiple covariates the performance of rta is compared to the classical method of forward stepwise regression the results of two simulation studies in which the true interactions are modeled as threshold interactions show that rta detects the interactions in a higher number of cases 82 3 in the first simulation study and 52 3 in the second than stepwise regression 56 5 and 20 5 in a real data example the final rta model has a higher cross validated variance accounted for 29 8 than the stepwise regression model 12 5 all of these results indicate that rta is a promising alternative method for demonstrating differential effectiveness of treatments

the asymptotically commuting bounded approximation property of banach spaces abstract we introduce and study the asymptotically commuting bounded approximation property of banach spaces this property is e g enjoyed by any dual space with the bounded approximation property the principal result is the following if a banach space x has the asymptotically commuting bounded approximation property then x is saturated with locally complemented separable subspaces enjoying the commuting bounded approximation property

lifting bounded approximation properties from banach spaces to their dual spaces based on a new reformulation of the bounded approximation property we develop a unified approach to the lifting of bounded approximation properties from a banach space x to its dual x this encompasses cases when x has the unique extension property or x is extendably locally reflexive in particular it is shown that the unique extension property of x permits to lift the metric a approximation property from x to x for any operator ideal a and that there exists a banach space x such that x x are extendably locally reflexive but x x are not

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

the norm of sums of independent noncommutative random variables in lp l1 we investigate the norm of sums of independent vector valued random variables in noncommutative lp spaces this allows us to obtain a uniform family of complete embeddings of the schatten class s n q in sp m q with optimal order m n 2 using these embeddings we show the surprising fact that the sharp type cotype index in the sense of operator spaces for lp 0 1 is min p p 0 max p p 0 similar techniques are used to show that the operator space notions of b convexity and k convexity are equivalent

colp spaces the local structure of non commutative lp spaces abstract developing the theory of col p spaces a variation of the non commutative analogue of l p spaces we provide new tools to investigate the local structure of non commutative l p spaces under mild assumptions on the underlying von neumann algebras non commutative l p spaces with grothendieck s approximation property behave locally like the space of matrices equipped with the p norm of the sequences of their singular values as applications we obtain a basis for non commutative l p spaces associated with hyperfinite von neumann algebras with separable predual von neumann algebras generated by free groups and obtain a basis for separable nuclear c algebras

representations of function algebras abstract operator spaces and banach space geometry let g be the closed unit ball of some norm on cn and let a g be the closure of the polynomials in the sup norm we prove that if n 5 then there is a contractive representation of a g as operators on a hilbert space which is not completely contractive our technique involves introducing a numerical invariant x for a normed space x which measures the difference between the minimal operator space structure which can be assigned to x min x and the maximal structure max x we estimate x using banach space techniques we also prove that if x is any infinite dimensional subspace of the space of continuous functions on a compact hausdorff space then there exists a bounded linear map on x which is not completely bounded

on the local lifting property for operator spaces we study the local lifting property for operator spaces this is a natural non commutative analogue of the banach space local lifting property but is very different from the local lifting property studied in c algebra theory we show that an operator space has the local lifting property if and only if it is an l 1 space these operator space are completely isomorphic to the operator subspaces of the operator preduals of von neumann algebras and thus locally reflexive moreover we show that an operator space v has the local lifting property if and only if its operator space dual v is injective

homotopy fixed point methods for lie groups and finite loop spaces a loop space x is by definition a triple x bx e in which x is a space bx is a connected pointed space and e x qbx is a homotopy equivalence from x to the space qbx of based loops in bx we will say that a loop space x is finite if the integral homology h x z is finitely generated as a graded abelian group i e if x appears at least homologically to be a finite complex in this paper we prove the following theorem

extension properties for the space of compact operators let z be a fixed separable operator space x y general separable operator spaces and t x z a completely bounded map z is said to have the complete separable extension property csep if every such map admits a completely bounded extension to y and the mixed separable extension property msep if every such t admits a bounded extension to y finally z is said to have the complete separable complementation property cscp if z is locally reflexive and t admits a completely bounded extension to y provided y is locally reflexive and t is a complete surjective isomorphism let k denote the space of compact operators on separable hilbert space and k0 the c0 sum of mn s the space of small compact operators it is proved that k has the cscp using the second author s previous result that k0 has this property a new proof is given for the result due to e kirchberg that k0 and hence k fails the csep it remains an open question if k has the msep it is proved this is equivalent to whether k0 has this property a new banach space concept extendable local reflexivity elr is introduced to study this problem further complements and open problems are discussed

multilevel logistic regression for polytomous data and rankings we propose a unifying framework for multilevel modeling of polytomous data and rankings accommodating dependence induced by factor and or random coefficient structures at different levels the framework subsumes a wide range of models proposed in disparate methodological literatures partial and tied rankings alternative specific explanatory variables and alternative sets varying across units are handled the problem of identification is addressed we develop an estimation and prediction methodology for the model framework which is implemented in the generally available gllamm software the methodology is applied to party choice and rankings from the 1987 1992 panel of the british election study three levels are considered elections voters and constituencies

dual problems for weak and quasi approximation properties abstract it is shown that for the separable dual x of a banach space x if x has the weak approximation property then x has the metric quasi approximation property using this it is shown that for the separable dual x of a banach space x the quasi approximation property and metric quasi approximation property are inherited from x to x and for a separable and reflexive banach space x x having the weak approximation property bounded weak approximation property quasi approximation property metric weak approximation property and metric quasi approximation property are equivalent also it is shown that the weak approximation property bounded weak approximation property and quasi approximation property are not inherited from a banach space x to x

contractive projections and operator spaces parallel to the study of finite dimensional banach spaces there is a growing interest in the corresponding local theory of operator spaces we define a family of hilbertian operator spaces h k n 1 k n generalizing the row and column hilbert spaces r n and c n and we show that an atomic subspace x c b h that is the range of a contractive projection on b h is isometrically completely contractive to an sum of the h k n and cartan factors of types 1 to 4 in particular for finite dimensional x this answers a question posed by oikhberg and rosenthal explicit in the proof is a classification up to complete isometry of atomic w closed jw triples without an infinite dimensional rank 1 w closed ideal

multivariate regression trees for analysis of abundance data summary multivariate regression tree methodology is developed and illustrated in a study predicting the abundance of several cooccurring plant species in missouri ozark forests the technique is a variation of the approach of segal 1992 for longitudinal data it has the potential to be applied to many different types of problems in which analysts want to predict the simultaneous cooccurrence of several dependent variables multivariate regression trees can also be used as an alternative to cluster analysis in situations where clusters are defined by a set of independent variables and the researcher wants clusters as homogeneous as possible with respect to a group of dependent variables

a new correlation coefficient for comparing and aggregating non strict and incomplete rankings abstract we introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non strict i e with ties and incomplete i e unknown preferences the correlation coefficient is designed to enforce a neutral treatment of incompleteness whereby no assumptions are made about individual preferences involving unranked objects the new measure which can be regarded as a generalization of the seminal kendall tau correlation coefficient is proven to satisfy a set of metric like axioms and to be equivalent to a recently developed ranking distance function associated with kemeny aggregation in an effort to further unify and enhance both robust ranking methodologies this work proves the equivalence of an additional distance and correlation coefficient pairing in the space of non strict incomplete rankings these connections induce new exact optimization methodologies a specialized branch and bound algorithm and an exact integer programming formulation moreover the bridging of these complementary theories reinforces the singular suitability of the featured correlation coefficient to solve the general consensus ranking problem the latter premise is bolstered by an accompanying set of experiments on random instances which are generated via a herein developed sampling technique connected with the classic mallows distribution of ranking data associated experiments with the branch and bound algorithm demonstrate that as data becomes noisier the featured correlation coefficient yields relatively fewer alternative optimal solutions and that the aggregate rankings tend to be closer to an underlying ground truth shared by a majority

ideals of operators and the metric approximation property abstract we prove that a banach space x has the metric approximation property if and only if f y x the space of all finite rank operators is an ideal in l y x the space of all bounded operators for every banach space y moreover x has the shrinking metric approximation property if and only if f x y is an ideal in l x y for every banach space y similar results are obtained for u ideals and the corresponding unconditional metric approximation properties

mixed effects analyses of rank ordered data this paper presents a synthesis of bock s 1972 nominal categories model and luce s 1959 choice model for mixed effects analyses of rank ordered data it is shown that the proposed ranking model is both parsimonious and flexible in accounting for preference heterogeneity as well as fixed and random effects of covariates relationships to other approaches including takane s 1987 ideal point discriminant model and croon s 1989 latent class version of luce s ranking model are also discussed the application focuses on a ranking study of behavioral traits that parents find desirable in children

on the p compact groups corresponding to the p adic reflection groups g q r n there exists an infinite family of p compact groups whose weyl groups correspond to the finite p adic pseudoreflection groups g q r n of family 2a in the clark ewing list in this paper we study these p compact groups in particular we construct an analog of the classical whitney sum map a family of monomorphisms and a spherical fibration which produces an analog of the classical j homomorphism finally we also describe a faithful complexification homomorphism from these p compact groups to the p completion of unitary compact lie groups

distance based ranking models on examine le modele de type mallows pour une distance generale et on etudie ensuite les distances pour lesquelles le modele peut etre decompose en facteurs representant des etapes independantes dans le processus de classement