on the kk theory and the e theory of amalgamated free products of c algebras abstract we establish six terms exact sequences relating the kk theory groups and the e theory groups of an amalgamated free product c algebra a 1 b a 2 to the respective groups of the three constituents a1 a2 and b in the kk theory case we assume that b is finite dimensional but in the e theory case only that b is nuclear or is the range of a conditional expectation in both a1 and a2 in particular we obtain the conjectured six terms exact sequence for the k theory of an amalgamated free product in this generality

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

non parametric tests for distributional treatment effect for randomly censored responses for a binary treatment 0 1 and the corresponding potential response y for the control group 0 and y 1 for the treatment group 1 one definition of no treatment effect is that y and y 1 follow the same distribution given a covariate vector x koul and schick have provided a non parametric test for no distributional effect when the realized response 1 v y y 1 is fully observed and the distribution of x is the same across the two groups this test is thus not applicable to censored responses nor to non experimental i e observational studies that entail different distributions of x across the two groups we propose x matched non parametric tests generalizing the test of koul and schick following an idea of gehan our tests are applicable to non experimental data with randomly censored responses in addition to these motivations the tests have several advantages first they have the intuitive appeal of comparing all available pairs across the treatment and control groups instead of selecting a number of matched controls or treated in the usual pair or multiple matching second whereas most matching estimators or tests have a non overlapping support of x problem across the two groups our tests have a built in protection against the problem third gehan s idea allows the tests to make good use of censored observations a simulation study is conducted and an empirical illustration for a job training effect on the duration of unemployment is provided

connes embedding problem and tsirelson s problem we show that tsirelson s problem concerning the set of quantum correlations and connes embedding problem on finite approximations in von neumann algebras known to be equivalent to kirchberg s qwep conjecture are essentially equivalent specifically tsirelson s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting c algebras connes embedding problem asks whether any separable ii1 factor is a subfactor of the ultrapower of the hyperfinite ii1 factor we show that an affirmative answer to connes question implies a positive answer to tsirelson s conversely a positive answer to a matrix valued version of tsirelson s problem implies a positive one to connes problem

free products of completely positive maps and spectral sets let f be the free group on n generators and for each word w e f let 1 wi be its length haagerup lo showed that for each 0 r 1 the function h wp r is a positive definite function on f consider the positive definite function q n rinl on h then the free product function cpi cpr on ff z h coincides with h and the result was extended this way by de michele and fig talamanca 7 and by boiejko 4 51 in s it is proved that the free product of the unital positive defined functions ui gi z z is still positive defined on the free product group gi the correspondence between the positive defined functions on a discrete group g and the completely positive maps on the full c algebra c g and the isomorphism c g g2 n c g z c g suggested we consider amalgamated products of unital linear maps on the amalgamated product of a family of unital c algebras over a c subalgebra in section 3 we prove that the amalgamated product of a family of unital completely positive b bimodule maps qi a c is completely positive on the biggest amalgamated free product i a i as an application of our main result in section 2 we obtain some results concerning the dilation of noncommutative families of operators

free products of c algebras small spatial free products of c algebras are constructed under certain conditions they have properties similar to those proved by paschke and salinas for the algebras c gi g2 where g1 g2 are discrete groups the freeproduct analogs of noncommutative bernoulli shifts are discussed 0 introduction let k be a field consider the category of unital algebras over k it is well known that this category admits coproducts free products of algebras 2 heuristically the free product of algebras is the algebra generated by them with no relations except for the identification of unit elements if k c the complex numbers and we consider unital algebras we can easily define a operation on the free products let a b be unital c algebras and a b their free product which is a unital algebra the question arises in what ways may one define a pre c norm on a b that extends the norms on a and b guided by analogy with tensor products we expect to have a choice among many pre c norms giving rise to many c free products of a and b one natural norm is 1c i i sup 1it c ih st representation of a b the representations of a b are in 1 1 correspondence with pairs of representations of a and b which act on the same hilbert space let a b be the completion of a b in this norm it is easy to see that this construction defines a coproduct in the category of c algebras and that a b is the biggest free product of a and b analogous to the biggest tensor product a 0 b if g 1 g2 are discrete groups we obtain c g1 c g2 c gi g2 where g1 g2 is the free product group and this is analogous to the relation c g1 0 c g2 c g1 x g2 this paper is motivated by the question is there a smallest c product a b in analogy to the smallest tensor product a b satisfying a relation cr gi g2 cr gi cr g2 received by the editors january 28 1981 and in revised form may 19 1981 1980 mathematics subject classification primary 46l05 secondary 46l55 1 982 american mathematical society 0002 9947 82 00001022 04 25

tsirelson s problem and asymptotically commuting unitary matrices in this paper we consider quantum correlations of bipartite systems having a slight interaction and reinterpret tsirelson s problem and hence kirchberg s and connes s conjectures in terms of finite dimensional asymptotically commuting positive operator valued measures we also consider the systems of asymptotically commuting unitary matrices and formulate the stronger kirchberg conjecture

estimating quantum chromatic numbers abstract we develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors we prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an sdp algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it we introduce the tracial rank of a graph a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank and prove that it is multiplicative we describe the tracial rank the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number the quantum chromatic number and the classical chromatic number respectively finally we present a new sdp algorithm that yields a parameter larger than the lovasz number and is yet a lower bound for the tracial rank of the graph we determine the precise value of the tracial rank of an odd cycle

models for noncommuting operators abstract this paper develops a model theory for a pair of noncommuting operators using backward shift operators on a fock space rota s theorem is generalized i e it is shown that any two bounded operators on a hilbert space are simultaneously similar to part of a pair of backward shift operators on a fock space these shift operators and the fock space framework are also used to develop a dilation theory for two noncommuting operators

non commutative functions and the non commutative free levy hincin formula abstract the paper is discussing infinite divisibility in the setting of operator valued boolean free and more general c free independences particularly using hilbert bimodule and non commutative function techniques we obtain analogues of the levy hincin integral representation for infinitely divisible real measures

infinite divisibility and a non commutative boolean to free bercovici pata bijection abstract we use the theory of fully matricial or non commutative functions to investigate infinite divisibility and limit theorems in operator valued non commutative probability our main result is an operator valued analogue for the bercovici pata bijection an important tool is voiculescu s subordination property for operator valued free convolution

the haagerup property for locally compact quantum groups the haagerup property for locally compact groups is generalised to the context of locally compact quantum groups with several equivalent characterisations in terms of the unitary representations and positive definite functions established in particular it is shown that a locally compact quantum group g has the haagerup property if and only if its mixing representations are dense in the space of all unitary representations for discrete g we characterise the haagerup property by the existence of a symmetric proper conditionally negative functional on the dual quantum group hat g by the existence of a real proper cocycle on g and further if g is also unimodular we show that the haagerup property is a von neumann property of g this extends results of akemann walter bekka cherix valette and jolissaint to the quantum setting and provides a connection to the recent work of brannan we use these characterisations to show that the haagerup property is preserved under free products of discrete quantum groups

spectral theory of fourier stieltjes algebras abstract in this paper we start studying spectral properties of the fourier stieltjes algebras largely following zafran s work on the algebra of measures on a locally compact group we show that for a large class of discrete groups the wiener pitt phenomenon occurs i e the spectrum of an element of the fourier stieltjes algebra is not captured by its range we also investigate the notions of absolute continuity and mutual singularity in this setting non commutativity forces upon us two distinct versions of support of an element indicating a crucial difference between this setup and the realm of abelian groups in spite of these difficulties we also show that one can introduce and use generalised characters to prove a criterion on belonging of a multiplicative linear functional to the shilov boundary of the fourier stieltjes algebra

equilibria of recurrent fuzzy systems unlike static fuzzy systems recurrent fuzzy systems are equipped with feedback loops and thus exhibit dynamic behaviors the dynamics of a recurrent fuzzy system is largely determined by its rule base the dynamic behavior of a significant subclass of recurrent fuzzy systems may be immediately deduced from their rule base without need for analyzing their mathematical description their equilibrium points may be readily identified and their stability behaviors investigated based on their rule base the investigations involved lead to convergence theorems and other statements that preclude chaotic dynamics

nonparametric estimation for a scale change with censored observations abstract nonparametric point and interval estimators of the ratio of two scale parameters are given for arbitrarily right censored data based on the idea of hodges and lehmann 1963 these estimators are defined in terms of rank test statistics for testing the equality of two survival distributions the asymptotic properties and efficiencies of estimators corresponding to the tests studied by gill 1980 are investigated