operator spaces and residually finite dimensional c algebras abstract for every operator space x the c algebra containing it in a universal way is residually finite dimensional that is has a separating family of finite dimensional representations in particular the free c algebra on any normed space is residually finite dimensional this is an extension of an earlier result by goodearl and menal and our short proof is based on a criterion due to exel and loring

similarity degree of fourier algebras we show that for a locally compact group g amongst a class which contains amenable and small invariant neighbourhood groups its fourier algebra a g satisfies a completely bounded version pisier s similarity property with similarity degree at most 2 specifically any completely bounded homomorphism a g b h admits an invertible s in b h for which s s 1 cb2 and s 1 s extends to a representation of the c algebra c0 g this significantly improves some results due to brannan and samei 2010 5 and brannan daws and samei 2013 4 we also note that a g has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if g is finite

the spectrum of prime ideals in tensor triangulated categories we define the spectrum of a tensor triangulated category k as the set of so called prime ideals endowed with a suitable topology in this very generality the spectrum is the universal space in which one can define supports for objects of k this construction is functorial with respect to all tensor triangulated functors several elementary properties of schemes hold for such spaces e g the existence of generic points or some quasi compactness locally trivial morphisms are proved to be nilpotent we establish in complete generality a classification of thick ideal subcategories in terms of arbitrary unions of closed subsets with quasi compact complements thomason s theorem for schemes mutatis mutandis we also equip this spectrum with a sheaf of rings turning it into a locally ringed space we compute examples and show that our spectrum unifies the schemes of algebraic geometry and the support varieties of modular representation theory

identification and estimation of econometric models with group interactions contextual factors and fixed effects this paper considers identification and estimation of structural interaction effects in a social interaction model the model allows unobservables in the group structure which may be correlated with included regressors we show that both the endogenous and exogenous interaction effects can be identified if there are sufficient variations in group sizes we consider the estimation of the model by the conditional maximum likelihood and instrumental variables methods for the case with large group sizes the possible identification can be weak in the sense that the estimates converge in distribution at low rates

a characterization of operator algebras abstract an operator algebra is a uniformly closed algebra of bounded operators on a hilbert space in this paper we give a characterization of unital operator algebras in terms of their matricial norm structure more precisely if a is an l matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1 then there is a completely isometric isomorphism of a onto a unital operator algebra indeed the multiplication on a need not be assumed to be associative for this conclusion to follow examples are given to show that the condition on the identity is necessary it follows from the above that the quotient of an operator algebra by a closed two sided ideal with the natural matricial structure is again an operator algebra up to complete isometric isomorphism

the spectrum of the equivariant stable homotopy category of a finite group we study the spectrum of prime ideals in the tensor triangulated category of compact equivariant spectra over a finite group we completely describe this spectrum as a set for all finite groups we also make significant progress in determining its topology and obtain a complete answer for groups of square free order for general finite groups we describe the topology up to an unresolved indeterminacy which we reduce to the case of p groups we then translate the remaining unresolved question into a new chromatic blue shift phenomenon for tate cohomology finally we draw conclusions on the classification of thick tensor ideals

the similarity problem for fourier algebras and corepresentations of group von neumann algebras let g be a locally compact group and let a g and vn g be its fourier algebra and group von neumann algebra respectively in this paper we consider the similarity problem for a g is every bounded representation of a g on a hilbert space h similar to a representation we show that the similarity problem for a g has a negative answer if and only if there is a bounded representation of a g which is not completely bounded for groups with small invariant neighborhoods i e sin groups we show that a representation a g b h is similar to a representation if and only if it is completely bounded this in particular implies that corepresentations of vn g associated to non degenerate completely bounded representations of a g are similar to unitary corepresentations we also show that if g is a sin maximally almost periodic or totally disconnected group then a representation of a g is a representation if and only if it is a complete contraction these results partially answer questions posed in effros and ruan 2003 7 and spronk 2002 25

asymptotics of cheeger constants and unitarisability of groups abstract given a group we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of cayley graphs of for increasingly large generating sets the connection hinges on an analytic invariant lit 0 which we call the littlewood exponent finiteness amenability unitarisability and the existence of free subgroups are related respectively to the thresholds 0 1 2 and for lit using graphical small cancellation theory we prove that there exist groups for which 1 lit further applications examples and problems are discussed

solution of the similarity problem for cyclic representations of c algebras in a paper from 1955 13 kadison considered the following problem is any bounded non selfadjoint representation 77 of a c algebra a on a hilbert space h similar to a representation i e does there exist an invertible operator t e b h such that tht t is a representation of a this problem is a natural counterpart to a problem considered by dixmier in 1950 9 is any bounded representation of a group g on a hilbert space similar to a unitary representation the group question was solved in the negative by kunze and stein in 1960 14 which in turn was based on previous work of ehrenpreis and mautner 21 the similarity problem for representations of c algebras is still open although a number of partial results have been obtained using the deep results of connes on infective von neumann algebras 7 and the characterization of nuclear c algebras given in 3 one gets the result fairly easily that every bounded representation of a nuclear c algebra is similar to a representation cf 2 th 3 5 and 5 th 4 1 the similarity problem for bounded cyclic representations of arbitrary c algebras was first considered by barnes in 1 he proved that when 77 is a bounded representation of a c algebra a on a hilbert space h such that 7v a and v a have a common cyclic vector i then there exists a closed infective operator t on h such that t and t are densely defined and such that x tht x t is a representation of a bunce sharpened this in 2 by proving that t can be chosen bounded but not necessarily with bounded inverse he also removed the condition that is cyclic for 7v a finally christensen proved in 5 that every irreducible bounded representation of a c algebra is similar to a representation these two results of bunce and christensen rely on an inequality due to pisier 16 cor 2 3 stating that when s is a bounded linear map from a c algebra a into a c algebra b then for all n e n and a an e a

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

corrigendum similarity degree of fourier algebras abstract we address two errors made in our paper 7 the most significant error is in theorem 1 1 we repair this error and show that the main result theorem 2 5 of 7 is true the second error is in one of our examples remark 2 4 iv and we partially resolve it

completely isometric representations of _ and let g be a locally compact group it is shown that there exists a natural completely isometric representation of the completely bounded fourier multiplier algebra m cb a g which is dual to the representation of the measure algebra m g on b l 2 g the image algebras of m g and m cb a g in cb b l 2 g are intrinsically characterized and some commutant theorems are proved it is also shown that for any amenable group g there is a natural completely isometric representation of ucb g on b l 2 g which can be regarded as a duality result of neufang s completely isometric representation theorem for luc g

measurable schur multipliers and completely bounded multipliers of the fourier algebras let g be a locally compact group and a g the fourier algebra of g from 17 in 24 herz de ned the space of herz schur multipliers b2 g he claimed that this space coincided with the space he denoted v g in his article 23 but o2ered no proof of this fact the completely bounded multipliers of the fourier algebra mcba g were de ned by de canniere and haagerup in 8 in was shown by bo zejko and fendler 7 that mcba g 1 4 b2 g isometrically unfortunately this result relies on unpublished work of gilbert entitled convolution operators and banach space tensor products i ii and iii but not widely available however there is a proof of the fact that mcba g 1 4 b2 g due to jolissaint 27 which relies on the representation theorem for completely bounded maps applied to the reduced c algebra c r g in this paper we prove an analogue of the fact that mcba g 1 4 b2 g in fact our result obtains that fact in the case that g is a discrete group and improves upon it in the respect that we obtain a complete isometry where both mcba g and b2 g are given natural operator space structures moreover we show that the natural module action of mcba g on the von neumann algebra generated by the left regular representation vn g extends completely isometrically to a normal action of mcba g on all of b l g the space of bounded operators on l g in fact the image of mcba g in the completely bounded normal maps on b l g consists of l1 g bimodule maps and can be characterised as a certain intrinsic invariant part amongst those maps we feel that our approach is interesting in and of itself since it makes systematic use of modern operator space theoretic techniques pioneered by blecher e2ros haagerup paulsen ruan and smith amongst others it thus gives a starting point for obtaining representations of completely bounded multipliers of kac algebras after 29 or of multipliers of locally compact quantum groups after vaes et al see 47 to support our approach in x 3 we describe the space of measurable schur multipliers v1 x for any suitable measure space x we develop the theory of v1 x fully and systematically our main tools for doing this are the results of smith 41 and blecher and smith 5 which characterise the normal completely bounded maps on the space of all bounded operators on a hilbert space which are module maps over a von neumann algebra we make great use of the weak haagerup tensor product of two von neumann algebras which is

tate cohomology and periodic localization of polynomial functors in this paper we show that goodwillie calculus as applied to functors from stable homotopy to itself interacts in striking ways with chromatic aspects of the stable category localized at a fixed prime p let t n be the telescope of a v n self map of a finite s module of type n the periodicity theorem of hopkins and smith implies that the bousfield localization functor associated to t n is independent of choices goodwillie s general theory says that to any homotopy functor f from s modules to s modules there is an associated tower under f p d f such that f p d f is the universal arrow to a d excisive functor our first main theorem says that p d f pd 1f always admits a homotopy section after localization with respect to t n and so also after localization with respect to morava k theory k n thus after periodic localization polynomial functors split as the product of their homogeneous factors this theorem follows from our second main theorem which is equivalent to the following for any finite group g the tate spectrum mathcal t g t n is weakly contractible this strengthens and extends previous theorems of greenlees sadofsky hovey sadofsky and mahowald shick the periodicity theorem is used in an essential way in our proof the connection between the two theorems is via a reformulation of a result of mccarthy on dual calculus

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

estimation of spatial autoregressive panel data models with fixed effects this paper establishes asymptotic properties of quasi maximum likelihood estimators for sar panel data models with fixed effects and sar disturbances a direct approach is to estimate all the parameters including the fixed effects because of the incidental parameter problem some parameter estimators may be inconsistent or their distributions are not properly centered we propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions for the model with individual effects only the direct approach does not yield a consistent estimator of the variance parameter unless t is large but the estimators for other common parameters are the same as those of the transformation approach we also consider the estimation of the model with both individual and time effects

self duality for the haagerup tensor product and hilbert space factorizations d blecher and v paulsen showed that the haagerup tensor product v h w for operator spaces v and w preserves inclusions it is proved to also preserve complete quotient maps and to be self dual in the sense that it induces the haagerup norm on the algebraic tensor product v w the full operator dual space v h w is computed it coincides with the natural operator space gg2 v w of maps v w which have completely bounded factorizations through hilbert spaces with vectors identified with row matrices more generally one has the natural complete isometry gg2 v h w x gg2 v gg2 w x given hilbert spaces h and k with vectors regarded as column matrices it is shown that one may identify the operator spaces b h k and cb h k

on the similarity problem for locally compact quantum groups abstract a well known theorem of day and dixmier states that any uniformly bounded representation of an amenable locally compact group g on a hilbert space is similar to a unitary representation within the category of locally compact quantum groups the conjectural analogue of the day dixmier theorem is that every completely bounded hilbert space representation of the convolution algebra of an amenable locally compact quantum group should be similar to a representation we prove that this conjecture is false for a large class of non kac type compact quantum groups including all q deformations of compact simply connected semisimple lie groups on the other hand within the kac framework we prove that the day dixmier theorem does indeed hold for several new classes of examples including amenable discrete quantum groups of kac type

a noncommutative amir cambern theorem for von neumann algebras and nuclear c algebras abstract we prove that von neumann algebras and separable nuclear c algebras are stable for the banach mazur cb distance a technical step is to show that unital almost completely isometric maps between c algebras are almost multiplicative and almost selfadjoint also as an intermediate result we compare the banach mazur cb distance and the kadison kastler distance finally we show that if two c algebras are close enough for the cb distance then they have comparable length

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

the balmer spectrum of the equivariant homotopy category of a finite abelian group for a finite abelian group a we determine the balmer spectrum of mathrm sp a omega the compact objects in genuine a spectra this generalizes the case a mathbb z p mathbb z due to balmer and sanders invent math 208 1 283 326 2017 by establishing a corrected version of their hbox log p conjecture for abelian groups we also work out the consequences for the chromatic type of fixed points and establish a generalization of kuhn s blue shift theorem for tate constructions kuhn in invent math 157 2 345 370 2004

representations of completely bounded multilinear operators a deli ion of a completely bounded multilinear operator from one c algebra into another is introduced each completely bounded multilinear operator from a algebra into the algebra of bounded linear operators on a hilbert space is shown to be representable in terms of representations of the c algebra and interlacing operators this result extends wittstock s theorem that decomposes a completely bounded linear operator from a c algebra into an injective c algebra into completely positive linear operators 0 1987 academic press inc stinespring s theorem gives a useful representation for a completely positive linear operator from a c algebra into the algebra bl h for continuous linear operators on a hilbert space h 12 11 using this representation with wittstock s theorem that decomposes a completely bounded linear operator as a finite linear combination of completely positive linear operators 14 lo one obtains a representation of a completely bounded linear operator from a c algebra into bl h our main result is a representation theorem for completely bounded multilinear operators from a c algebra into bl h which generalizes this representation of completely bounded linear operators corollaries give multilinear generalizations of several results known for completely bounded linear operators we shall briefly describe the type of representations to be 151

ideals of a c algebra generated by an operator algebra in this paper we consider ideals of a c algebra c b generated by an operator algebra b a closed ideal j subset of c b is called a k boundary ideal if the restriction of the quotient map on b has a completely bounded inverse with cb norm equal to k 1 for k 1 one gets the notion of boundary ideals introduced by arveson we study properties of the k boundary ideals and characterize them in the case when operator algebra lambda norms itself several reformulations of the kadison similarity problem are given in particular the affirmative answer to this problem is equivalent to the statement that every bounded homomorphism from c b onto b which is a projection on b is completely bounded moreover we prove that kadison s similarity problem is decided on one particular c algebra which is a completion of the double of m 2 c

amenability and virtual diagonals for von neumann algebras abstract it is shown that a certain universal bimodule over a von neumann algebra is automatically normal this leads to a simple direct proof of haagerup s result that a von neumann algebra is amenable or equivalently injective if and only if it has a normal virtual diagonal haagerup has used this fact to prove that nuclear c algebras are amenable

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

finite von neumann algebra factors with property γ abstract techniques introduced by g pisier in his proof that finite von neumann factors with property have length at most 5 are modified to prove that the length is 3 it is proved that if such a factor is a complemented subspace of a larger c algebra then there exists a projection of norm one from the larger algebra onto the smaller and a new proof of the fact that the continuous hochschild cohomology group h2c m m vanishes is also included

generalized tensor idempotents and the telescope conjecture we transpose rickard s construction of idempotent representations to the general context of tensor triangulated categories we connect our construction to the telescope conjecture and prove that the latter is of local nature as an illustration we extend the affine telescope theorem of neeman to arbitrary noetherian schemes we also develop supports for non compact objects

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

the similarity degree of an operator algebra ii for every integer d ge 1 there is a unital closed subalgebra a d subset b h with similarity degree equal precisely to d in the sense of our previous paper this means that for any unital homomorphism u colon a d to b h we have u cb le k u d with k 0 independent of u and the exponent d in this estimate cannot be improved the proof that the degree is larger than d 1 crucially uses an upper bound for the norms of certain gaussian random matrices due to haagerup and thorbjornsen we also include several complements to our previous publications on the same subject

separability and triangulated categories abstract we prove that the category of modules over a separable ring object in a tensor triangulated category admits a unique structure of triangulated category which is compatible with the original one this applies in particular to etale algebras more generally we do this for exact separable monads

pi supports for modules for finite group schemes we introduce the space g of equivalence classes of points of a finite group scheme g and associate a subspace g m to any g module m our results extend to arbitrary finite group schemes g over arbitrary fields k of positive characteristic and to arbitrarily large g modules the basic results about cohomological support varieties and their interpretation in terms of representation theory in particular we prove that the projectivity of any possibly infinite dimensional g module can be detected by its restriction along points of g unlike the cohomological support variety of a g module m the invariant m 7 g m satisfies good properties for all modules thereby enabling us to determine the thick tensor ideal subcategories of the stable module category of finite dimensional g modules finally using the stable module category of g we provide g with the structure of a ringed space which we show to be isomorphic to the scheme projh g k

multilinear maps and tensor norms on operator systems abstract we extend work of christensen and sinclair on completely bounded multilinear forms to the case of subspaces of c algebras and obtain a representation theorem and a hahn banach extension theorem for such maps in the second part of the paper the haagerup norms on tensor products are investigated and we obtain new characterizations of these quantities

subspaces of c algebras abstract basic properties of matricially normed spaces are considered and a simple matrix norm characterization of the subspaces of c algebras is given the latter result is used to study the haagerup tensor products and quotients of such subspaces

on the nonexistence of elements of kervaire invariant one we show that the kervaire invariant one elements j 2j 1 2s exist only for j 6 by browder s theorem this means that smooth framed manifolds of kervaire invariant one exist only in dimensions 2 6 14 30 62 and possibly 126 except for dimension 126 this resolves a longstanding problem in algebraic topology