3 manifold groups with the finitely generated intersection property in this paper first we consider whether the fundamental groups of certain geometric 3 manifolds have fgip or not next we give the sufficient conditions that fgip for 3 manifold groups is preserved under torus sums or annulus sums and connect this result with a conjecture by hempel 4

herz schur multipliers of dynamical systems abstract we extend the notion of a herz schur multiplier to the setting of non commutative dynamical systems given a c algebra a a locally compact group g and an action of g on a we define transformations on the reduced crossed product of a by which in the case a c reduce to the classical herz schur multipliers we introduce schur a multipliers establish a characterisation that generalises the classical descriptions of schur multipliers and present a transference theorem in the new setting identifying isometrically the herz schur multipliers of the dynamical system a g with the invariant part of the schur a multipliers we discuss special classes of herz schur multipliers in particular those associated to a locally compact abelian group g and its canonical action on the c algebra c of the dual group

on pro p analogues of limit groups via extensions of centralizers we begin a study of a pro p analogue of limit groups via extensions of centralizers and call mathcal l this new class of pro p groups we show that the pro p groups of mathcal l have finite cohomological dimension type fp and non positive euler characteristic among the group theoretic properties it is proved that they are free by torsion free nilpotent and if non abelian do not have a finitely generated non trivial normal subgroup of infinite index furthermore it is shown that every 2 generated pro p group in the class mathcal l is either free pro p or abelian

submultiplicativity and the hanna neumann conjecture in this article we dene submultiplicativity of 2 numbers in the category of complexes over a given complex x which generalizes the statement of the strengthened hanna neumann conjecture shnc in the case when is a left orderable group and x is a free complex we prove submultiplicativity for the subcategory consisting of ordered leafages over x with an additional analytic assumption called the deep fall property we show that the deep fall property is satised for graphs this implies shnc

operator biflatness of the fourier algebra and approximate indicators for subgroups abstract we investigate if for a locally compact group g the fourier algebra a g is biflat in the sense of quantized banach homology a central role in our investigation is played by the notion of an approximate indicator of a closed subgroup of g the fourier algebra is operator biflat whenever the diagonal in g g has an approximate indicator although we have been unable to settle the question of whether a g is always operator biflat we show that for g sl 3 c the diagonal in g g fails to have an approximate indicator

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

optimal and efficient crossover designs for comparing test treatments with a control treatment this paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t 1 among other results it specifies sufficient conditions for a crossover design to be simultaneously a optimal and mv optimal in a very large and appealing class of crossover designs it is expected that these optimal designs are highly efficient in the entire class of crossover designs some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs the model robustness of these newly discovered crossover designs is discussed

on the intersection of subgroups of a free group the hanna neumann conjecture says that the intersection of subgroups of rankn 1 andm 1 of a free group has rank at mostnm 1 this paper proves the conjecture for the casem 1 see theorem 1 our methods imply that the strengthened hanna neumann conjecture is also true in this case theorem 2

grothendieck s theorem past and present probably the most famous of grothendieck s contributions to banach space theory is the result that he himself described as the fundamental theorem in the metric theory of tensor products that is now commonly referred to as grothendieck s theorem gt in short or sometimes as grothendieck s inequality this had a major impact first in banach space theory roughly after 1968 then later on in c algebra theory roughly after 1978 more recently in this millennium a new version of gt has been successfully developed in the framework of operator spaces or non commutative banach spaces in addition gt independently surfaced in several quite unrelated fields in connection with bell s inequality in quantum mechanics in graph theory where the grothendieck constant of a graph has been introduced and in computer science where the grothendieck inequality is invoked to replace certain np hard problems by others that can be treated by semidefinite programming and hence solved in polynomial time in this expository paper we present a review of all these topics starting from the original gt we concentrate on the more recent developments and merely outline those of the first banach space period since detailed accounts of that are already available for instance the author s 1986 cbms notes

the impact of baseline covariates on the efficiency of statistical analyses of crossover designs we investigate the impact of baseline covariates on the efficiency of statistical analyses of crossover designs for practical considerations we contemplate two different baseline methods study baselines and period dependent baselines for each baseline method we establish analytical upper bounds for the relative efficiency of a large class of crossover designs the totally balanced designs under a model with the baseline covariates as compared with the model without the baseline covariates we present numerical details based on these bounds for assorted scenarios and reveal implications of these results copyright 2012 john wiley sons ltd

optimal two period repeated measurement designs with two or more treatments summary for two period repeated measurement designs for comparing t 2 treatments we discuss universally optimal designs when the number of subjects n is a multiple of t2 and some cases when n is a multiple of t we examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs in addition efficiencies of the universally optimal designs obtained by hedayat zhao 1990 are examined under both fixed subject and random subject effect model assumptions

compactness properties of operator multipliers abstract we continue the study of multidimensional operator multipliers initiated in k juschenko i g todorov l turowska multidimensional operator multipliers trans amer math soc in press we introduce the notion of the symbol of an operator multiplier we characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers we give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two c algebras is automatically compact we give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the c algebra of compact operators in terms of tensor products generalising results of saar h saar kompakte vollstandig beschrankte abbildungen mit werten in einer nuklearen c algebra diplomarbeit universitat des saarlandes saarbrucken 1982

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

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

operator synthesis i synthetic sets bilattices and tensor algebras abstract the interplay between the invariant subspace theory and spectral synthesis for locally compact abelian group discovered by arveson ann of math 2 100 1974 433 is extended to include other topics as harmonic analysis for varopoulos algebras and approximation by projection valued measures we propose a coordinate approach which nevertheless does not use the technique of pseudo integral operators as well as a coordinate free one which allows to extend to non separable spaces some important results and constructions of arveson we solve some problems posed in arveson 1974

operator space structure on feichtinger s segal algebra abstract we extend the definition from the class of abelian groups to a general locally compact group g of feichtinger s remarkable segal algebra s 0 g in order to obtain functorial properties for non abelian groups in particular a tensor product formula we endow s 0 g with an operator space structure with this structure s 0 g is simultaneously an operator segal algebra of the fourier algebra a g and of the group algebra l 1 g we show that this operator space structure is consistent with the major functorial properties i s 0 g s 0 h s 0 g h completely isomorphically operator projective tensor product if h is another locally compact group ii the restriction map u u h s 0 g s 0 h is completely surjective if h is a closed subgroup and iii n s 0 g s 0 g n is completely surjective where n is a normal subgroup and n u s n n u s n d n we also show that s 0 g is an invariant for g when it is treated simultaneously as a pointwise algebra and a convolutive algebra

universal optimality of balanced uniform crossover designs kunert ann statist 12 1984 1006 1017 proved that in the class of repeated measurement designs based on t treatments p t periods and n t experimental units a balanced uniform design is universally optimal for direct treatment effects if t 3 and 1 or if t 6 and 2 this result is generalized to t 3 as long as t 1 2

the intersection of subgroups in free groups and linear programming we study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming we prove that if h 1 is a finitely generated subgroup of a free group f then the wn coefficient sigma h 1 of h 1 is rational and can be computed in deterministic exponential time in the size of h 1 this coefficient sigma h 1 is the minimal nonnegative real number such that for every finitely generated subgroup h 2 of f it is true that bar mathrm r h 1 h 2 le sigma h 1 bar mathrm r h 1 bar mathrm r h 2 where bar mathrm r h max mathrm r h 1 0 is the reduced rank of h mathrm r h is the rank of h and bar mathrm r h 1 h 2 is the reduced rank of the generalized intersection of h 1 and h 2 we also show the existence of a subgroup h 2 h 2 h 1 of f such that bar mathrm r h 1 h 2 sigma h 1 bar mathrm r h 1 bar mathrm r h 2 the stallings graph gamma h 2 of h 2 has at most doubly exponential size in the size of h 1 and gamma h 2 can be constructed in exponential time in the size of h 1

demuskin fields with valuations we study the arithmetic structure of fields f of characteristic neq p containing a primitive pth root of unity for which the maximal pro p galois group of f is a finitely generated demuskin group

weighted group algebras on groups of polynomial growth let g be a compactly generated group of polynomial growth and a weight function on g for a large class of weights we characterize symmetry of the weighted group algebra l 1 g in particular if the weight is sub exponential then the algebra l 1 g is symmetric for these weights we develop a functional calculus on a total part of l 1 g and use it to prove the wiener property

equivalence of the strengthened hanna neumann conjecture and the amalgamated graph conjecture we show that walter neumann s strengthened form of hanna neumann s conjecture on the best possible upper bound for the rank of the intersection of two subgroups of a free group is equivalent to a conjecture on the best possible upper bound for the number of edges in a bipartite graph with a certain weak symmetry condition we illustrate the usefulness of this equivalence by deriving relatively easily certain previously known results

examples of retracts in free groups that are not the fixed subgroup of any automorphism let n be an arbitrary cardinal and let fn be a free group of rank n the flxed subgroup of an endomorphismof fn is the subgroup of elements in fn flxed by in this paper the relationship between the family of flxed subgroups of endomorphisms of fn and the family of flxed subgroups of automorphisms of fn will be studied we prove that these two families of subgroups do not coincide for n 3 by showing an inflnite sequence of explicit examples of retracts of fn and so flxed subgroups of endomorphisms of fn which are not flxed subgroups of any automorphism of fn

ascending chains of finitely generated subgroups abstract we show that a nonempty family of n generated subgroups of a pro p group has a maximal element this suggests that noetherian induction can be used to discover new features of finitely generated subgroups of pro p groups to demonstrate this we show that in various pro p groups e g free pro p groups nonsolvable demushkin groups the commensurator of a finitely generated subgroup h 1 is the greatest subgroup of containing h as an open subgroup we also show that an ascending chain of n generated subgroups of a limit group must terminate this extends the analogous result for free groups proved by takahasi higman and kapovich myasnikov

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

demuskin groups galois modules and the elementary type conjecture abstract let p be a prime and f p the maximal p extension of a field f containing a primitive pth root of unity we give a new characterization of demuskin groups among galois groups gal f p f when p 2 and assuming the elementary type conjecture when p 2 as well this characterization is in terms of the structure as galois modules of the galois cohomology of index p subgroups of gal f p f

completely bounded module maps and the haagerup tensor product abstract we obtain a representation theorem for module maps defined on the algebra k h of compact operators this is used to show that the haagerup tensor product of two operator algebras enjoys strong versions of tomita s commutant theorem and the slice map property we also give a general theorem concerning the automatic complete boundedness of module maps

ideal structure of beurling algebras on fc groups abstract it is proved that for an fc group g the beurling algebra l 1 g is regular if and only if is non quasianalytic as an application the wiener property is deduced further for a compact fd group g points in prim l 1 g are shown to be spectral provided that satisfies shilov s conditions

on the connection between sets of operator synthesis and sets of spectral synthesis for locally compact groups we extend the results by froelich and spronk and turowska on the connection between operator synthesis and spectral synthesis for a g to second countable locally compact groups g this gives us another proof that one point subset of g is a set of spectral synthesis and that any closed subgroup is a set of local spectral synthesis furthermore we show that non triangular sets are strong operator ditkin sets and we establish a connection between operator ditkin sets and ditkin sets these results are applied to prove that any closed subgroup of g is a local ditkin set

universal optimality for selected crossover designs hedayat and yang earlier proved that balanced uniform designs in the entire class of crossover designs based on t treatments n subjects and p t periods are universally optimal when n t t 1 2 surprisingly in the class of crossover designs with t treatments and p t periods a balanced uniform design may not be universally optimal if the number of subjects exceeds t t 1 2 this article among other results shows that a a balanced uniform design is universally optimal in the entire class of crossover designs withp t as long as n is not greater than t t 2 2 and 3 t 12 b a balanced uniform design with n 2t t 3 and p t is universally optimal in the entire class of crossover designs with n 2t and p t and c for the case where p t the design suggested by stufken is universally optimal thus completing kushner s result that a stufken design is universally optimal if n is divisible by t p 1

beurling fourier algebras on compact groups spectral theory for a compact group g we define the beurling fourier algebra a omega g on g for weights omega defined on the dual what g and taking positive values the classical fourier algebra corresponds to the case omega is the constant weight 1 we study the gelfand spectrum of the algebra realizing it as a subset of the complexification g mathbb c defined by mckennon and cartwright and mcmullen in many cases such as for polynomial weights the spectrum is simply g we discuss the questions when the algebra a omega g is symmetric and regular we also obtain various results concerning spectral synthesis for a omega g

on p approximation properties for p operator spaces abstract this paper has a two fold purpose let 1 p we first introduce the p operator space injective tensor product and study various properties related to this tensor product including the p operator space approximation property for p operator spaces on l p spaces we then apply these properties to the study of the pseudofunction algebra pf p g the pseudomeasure algebra pm p g and the figa talamanca herz algebra a p g of a locally compact group g we show that if g is a discrete group then most of approximation properties for the reduced group c algebra c g the group von neumann algebra vn g and the fourier algebra a g related to amenability weak amenability and approximation property of g have the natural p analogues for pf p g pm p g and a p g respectively the p completely bounded multiplier algebra m cb a p g plays an important role in this work

towards the hanna neumann conjecture using dicks method the hanna neumann conjecture states that the intersection of two nontrivial subgroups of rankk 1 andl 1 of a free group has rank at mostkl 1 in a recent paper 3 w dicks proved that a strengthened form of this conjecture is equivalent to his amalgamated graph conjecture he used this equivalence to reprove all known upper bounds on the rank of the intersection we use his method to improve these bounds in particular we prove an upper bound of 2kl k l 1 for the rank of the intersection above k l 2 improving the earlier 2kl min k l bound of 1

free by demushkin pro p groups we give an example of a short exact sequence 1 n g d 1 of pro p groups such that the cohomological dimension cd g 2 g is topologically finitely generated n is a free pro p group of infinite rank d is a demushkin group for every closed subgroup s of g containing n and any natural number n the inflation map open image in new window is an isomorphism but g is not a free pro p product of a free pro p group by a demushkin group this is a group theoretic version of a question raised by t wurfel for some special galois groups

idempotents with small norms let be a locally compact group we answer two questions left open in 8 and 10 i for abelian we prove that if s b is an idempotent with norm s 43 then s is the union of two cosets of an open subgroup of ii for general we prove that if s mcba is an idempotent with norm s cb 1 22 then s is an open coset in

compact operators invariant subspaces and spectral synthesis let l be a subspace lattice which contains a sequence pn of commuting projections such that for any subsequence pni vpni i and pni 0 then alg l k h 0 suppose g is a compact abelian group and e g is a closed set there is a family le of commutative subspace lattices for which alg le k h 0 precisely when e is a set of multiplicity in the sense of harmonic analysis by showing that the graph of is a set of uniqueness in 2 2 we obtain a thin set proof that alg 2 m12 contains no nonzero compact operators for an important class of sets k g gamin k amax k iff k is a set of spectral synthesis in the group g x g it follows that if e1and e2 are sets of spectral synthesis in g then alg pe1 bo alg pe2 alg pe1 pe2iff e1 e2 is a set of spectral synthesis in g x g and if semigroups 1 and 2 are sets of spectral synthesis in g then alg 1 bo alg 2 alg 1 2iff 1 2 is a set of spectral synthesis in g g the operator algebra alg p1 p2 is synthetic iff for all n alg p1 pn is synthetic this implies that the operator algebras alg 2 mp are synthetic

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

fully residually free pro p groups abstract we prove that the pro p completion of the orientable surface group of genus d is residually free pro p if d is even or p 2 the case when p 2 odd d 1 is still open

a property of bp g applications to convolution operators a new property of b p g permits to obtain an approximation theorem for p convolution operators and a non commutative version of the lohoues monomorphism theorem concerning the norm closure of the set of all p convolution operators with compact support c 2008 elsevier inc all rights reserved

on the rank of the intersection of free subgroups in virtually free groups abstract we prove an estimate for the rank of the intersection of free subgroups in virtually free groups which is analogous to the hanna neumann inequality for subgroups in a free group and to the s v ivanov estimate for subgroups in free products of groups we also prove a more general estimate for the rank of the intersection of free subgroups in the fundamental group of a finite graph of groups with finite edge groups

ideals of a g and bimodules over maximal abelian selfadjoint algebras this paper is concerned with weak closed masa bimodules generated by a g invariant subspaces of vn g an annihilator formula is established which is used to characterise the weak closed subspaces of b l2 g which are invariant under both schur multipliers and a canonical action of m g on b l2 g via completely bounded maps we study the special cases of extremal ideals with a given null set and for a large class of groups we establish a link between relative spectral synthesis and relative operator synthesis

the sylow subgroups of the absolute galois group gal q abstract we describe the l sylow subgroups of gal q for an odd prime l by observing and studying their decomposition as f z l where f is a free pro l group and z l are the l adic integers we determine the finite z l quotients of f and more generally show that every split embedding problem of z l groups for f is solvable moreover we analyze the z l action on generators of f

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

a variational approach to optimal two treatment crossover designs application to carryover effect models abstract a variational method is used to obtain sufficient conditions for an optimal two treatment p period design given a repeated measures model with arbitrary within subject covariance the design minimizes the variance of the estimator of treatment differences over all possible allocations of n subjects to the 2 p possible treatment sequences the method is applied to a model that includes carryover effects when subject effects are random with equicorrelated observations designs are optimal if they are a strongly balanced b uniform on the rows and c either uniform on the subjects p is even and greater than 2 or uniform on the first p 1 periods if p is odd for two periods the optimal design is ab ba aa bb the same designs are optimal when baseline measurements are obtained in each period baseline observations improve efficiency considerably for p 2 only slightly for p odd and are of no help for p even and greater than 2 a second model of errors in which a subject s response ha

optimal and efficient repeated measurements designs for uncorrelated observations abstract in repeated measurements crossover or changeover designs experimental subjects units are repeatedly exposed to treatments effects of treatments from one period that extend into the next are called carryover or residual effects in exact design theory designs that are universally optimal in the presence of carryover effects have been found when a subject s responses are uncorrelated however the results are valid only for restricted values of t the number of treatments p the number of periods and n the number of subjects in other optimality results the competing class of designs is a subset of the full class of repeated measurements designs these restrictions hinder applicability in the setting of approximate design theory kushner 1997b developed a new approach valid even for correlated responses here the results are specialized to the case of uncorrelated responses linear equations are given that determine all universally or a and d optimal repeated measurements desig

on the kurosh rank of the intersection of subgroups in free products of groups abstract the kurosh rank r k h of a subgroup h of a free product i g of groups g i is defined accordingly to the classic kurosh subgroup theorem as the number of free factors of h we prove that if h 1 h 2 are subgroups of i g and h 1 h 2 have finite kurosh rank then r k h 1 h 2 2 q q 2 r k h 1 r k h 2 6 r k h 1 r k h 2 where r k h max r k h 1 0 q is the minimum of orders 2 of finite subgroups of groups g i q if there are no such subgroups and q q 2 1 if q in particular if the factors g i are torsion free groups then r k h 1 h 2 2 r k h 1 r k h 2

optimal repeated measurements designs the linear optimality equations in approximate design theory necessary and sufficient conditions that a repeated measurements design be universally optimal are given as linear equations whose unknowns are the proportions of subjects on the treatment sequences both the number of periods and the number of treatments in the designs are arbitrary as is the covariance matrix of the normal response model the existence of universally optimal symmetric designs is proved the single linear equation which the proportions satisfy is given a formula for the information matrix of a universally optimal design is derived

mapping ideals of quantum group multipliers abstract we study the dual relationship between quantum group convolution maps l 1 g l g and completely bounded multipliers of g for a large class of locally compact quantum groups g we completely isomorphically identify the mapping ideal of row hilbert space factorizable convolution maps with m c b l 1 g yielding a quantum gilbert representation for completely bounded multipliers we also identify the mapping ideals of completely integral and completely nuclear convolution maps the latter coinciding with l 1 b g where b g is the quantum bohr compactification of g for quantum groups whose dual has bounded degree we show that the completely compact convolution maps coincide with c b g our techniques comprise a mixture of operator space theory and abstract harmonic analysis including fubini tensor products the non commutative grothendieck inequality quantum eberlein compactifications and a suitable notion of inner co amenable quantum group that we introduce and for which we exhibit examples from the bicrossed product construction our main results are new even in the setting of group von neumann algebras v n g for quasi sin locally compact groups g

topology of finite graphs this paper derives from a course in group theory which i gave at berkeley in 1982 i wanted to prove the standard theorems on free groups and discovered that after a few preliminaries the notion of locally injective map or immersion of graphs was very useful this enables one to see in an effective easy algorithmic way just what happens with finitely generated free groups one can understand in this way 1 howson s theorem that if a and b are finitely generated subgroups of a free group then a b is finitely generated and 2 m hall s theorem that finitely generated subgroups of free groups are closed in the profinite topology during this course s m gersten came up with a simple proof of h neumann s inequality on the ranks in howson s theorem one of the ideas in gersten s proof was to use core graphs graphs with no trees hanging on subsequently i found that some consequences of a paper of greenberg s could be proved using core graphs and covering translations of immersions the most striking such result is that if a and b are finitely generated subgroups of a free group and if a c b is of finite index in both a and b then a b is of finite index in a v b the subgroup generated by a ub

beurling fourier algebras operator amenability and arens regularity abstract we introduce the class of beurling fourier algebras on locally compact groups and show that they are non commutative analogs of classical beurling algebras we obtain various results with regard to the operator amenability operator weak amenability and arens regularity of beurling fourier algebras on compact groups and show that they behave very similarly to the classical beurling algebras of discrete groups we then apply our results to study explicitly the beurling fourier algebras on su 2 the 2 2 special unitary group we demonstrate that how beurling fourier algebras are closely connected to the amenability of the fourier algebra of su 2 another major consequence of our results is that our investigation allows us to construct families of unital infinite dimensional closed arens regular subalgebras of the fourier algebra of certain products of su 2

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

optimal and efficient crossover designs for test control study when subject effects are random we study crossover designs based on the criteria of a optimality and mv optimality under the model with random subject effects for the purpose of comparing several test treatments with a standard control treatment optimal and efficient designs are proposed and their efficiencies are also evaluated a family of totally balanced test control incomplete crossover designs based on a function of the ratio of the subject effect variance to the error variance are shown to be highly efficient and robust the results have interesting connections with those in hedayat and yang 2005 and hedayat stufken and yang 2006 the omitted proofs in the article are included in a supplemental material online

varieties of finite supersolvable groups with the m hall property the varieties in the title are shown to be precisely the product varieties gp ab d for some prime p and some positive integer d dividing p 1 here gp denotes the variety of all finite p groups and ab d the variety of all finite abelian groups of exponent dividing d it turns out that these are exactly those varieties h of supersolvable groups for which all finitely generated free pro h groups are freely indexed in the sense of lubotzky and van den dries several alternative characterizations of these varieties are presented some applications to formal language theory and finite monoid theory are also given among these is the determination of all supersolvable solutions h to the equations ph j h and j h jopen image in new windowh which is to the present date the most complete solution to a problem raised by pin another consequence of our results is that for each such variety h the monoid variety ph j h jopen image in new windowh has decidable membership

optimal and efficient crossover designs when subject effects are random most studies on optimal crossover designs are based on models that assume subject effects to be fixed effects in this article we identify and study optimal and efficient designs for a model with random subject effects with the number of periods not exceeding the number of treatments we find that totally balanced designs are universally optimal for treatment effects in a large subclass of competing designs however in the entire class of designs totally balanced designs are in general not optimal and their efficiency depends on the ratio of the subject effects variance and the error variance we develop tools to study the efficiency of totally balanced designs and to identify designs with higher efficiency

sets of multiplicity and closable multipliers on group algebras we undertake a detailed study of the sets of multiplicity in a second countable locally compact group g and their operator versions we establish a symbolic calculus for normal completely bounded maps from the space b l2 g of bounded linear operators on l2 g into the von neumann algebra vn g of g and use it to show that a closed subset e g is a set of multiplicity if and only if the set e s t g g ts 1 e is a set of operator multiplicity analogous results are established for m1 sets and m0 sets we show that the property of being a set of multiplicity is preserved under various operations including taking direct products and establish an inverse image theorem for such sets we characterise the sets of finite width that are also sets of operator multiplicity and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set we show that if g satisfies a mild approximation condition pointwise multiplication by a given measurable function g c defines a closable multiplier on the reduced c algebra view the mathml source of g if and only if schur multiplication by the function n g g c given by n s t ts 1 is a closable operator when viewed as a densely defined linear map on the space of compact operators on l2 g similar results are obtained for multipliers on vn g

optimal crossover designs in a model with self and mixed carryover effects we consider a variant of the usual model for crossover designs with carryover effects instead of assuming that the carryover effect of a treatment is the same regardless of the treatment in the next period the model assumes that the carryover effect of a treatment on itself is different from the carryover effect on other treatments for the traditional model optimal designs tend to have pairs of consecutive identical treatments for the model considered here they tend to avoid such pairs practitioners have long expressed reservations about designs that exhibit such pairs and about the traditional model the new model provides an attractive alternative that leads to appealing optimal designs

optimal design and refinement of the linera model with applications to repeated measurements designs the information matrices of one design in a finer and a simpler linear model are compared to each other the orthogonality condition ensuring that both matrices are equal is examined in the model for repeated measurements designs which was considered e g by cheng and wu 1980 examples of unbalanced designs fulfilling the orthogonality condition are shown to be optimum moreover nearly strongly balanced generalized latin squares are introduced and their universal optimality is proved if the numbers of units and periods are sufficiently large

completely bounded maps and invariant subspaces we provide a description of certain invariance properties of completely bounded bimodule maps in terms of their symbols if mathbb g is a locally compact quantum group we characterise the completely bounded l infty mathbb g bimodule maps that send c 0 hat mathbb g into l infty hat mathbb g in terms of the properties of the corresponding elements of the normal haagerup tensor product l infty mathbb g otimes sigma mathop mathrm h l infty mathbb g as a consequence we obtain an intrinsic characterisation of the normal completely bounded l infty mathbb g bimodule maps that leave l infty hat mathbb g invariant extending and unifying results formulated in the current literature separately for the commutative and the co commutative cases

some beurling fourier algebras on compact groups are operator algebras let g be a compact connected lie group the question of when a weighted fourier algebra on g is completely isomorphic to an operator algebra will be investigated in this paper we will demonstrate that the dimension of the group plays an important role in the question more precisely we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on g with the order of growth strictly bigger than the half of the dimension of the group the case of su n will be exam ined focusing more on the details including negative results the proof for the positive directions depends on a non commutative version of littlewood mul tiplier theory which we will develop in this paper and the negative directions will be taken care of by restricting to a maximal torus

on the determination of optimal designs for an interference model this paper generalizes kushner s method for finding optimal repeated measurements designs to find optimal designs under an interference model the model we assume is for a one dimensional layout without guard plots and with different left and right neighbor effects the resulting optimal designs may need many blocks or may not even exist as a finite design the results give lower bounds for optimality criteria on finite designs and the design structure can be used to suggest efficient small designs