the commutation theorem for tensor products over von neumann algebras abstract a general commutation theorem is proved for tensor products of von neumann algebras over common von neumann subalgebras roughly speaking if the non common parts of two von neumann algebras m 1 and m 2 on the same hilbert space are appropriately separated by commuting type i von neumann algebras n 1 and n 2 then the commutant of the von neumann algebra generated by m 1 and m 2 is generated by the relative commutants m 1 n 1 and m 2 n 2 as well as by the intersection of the commutants of all concerned von neumann algebras this theorem extends both tomita s classical commutation theorem and a splitting result in tensor products proved recently in the factor case by l ge and r v kadison applications are given to a decomposition criterion in ordinary tensor products and to a partial solution of a conjecture of s popa concerning the maximal injectivity of tensor products of maximal injective von neumann subalgebras

an inner amenable group whose von neumann algebra does not have property gamma we construct inner amenable groups g with infinite conjugacy classes and such that the associated ii1 factor has no non trivial asymptotically central elements i e does not have property gamma of murray and von neumann this solves a problem posed by effros in 1975

full factors and co amenable inclusions we show that if m is a full factor and n subset m is a co amenable subfactor with expectation then n is also full this answers a question of popa from 1986 we also generalize a theorem of tomatsu by showing that if m is a full factor and sigma g curvearrowright m is an outer action of a compact group g then sigma is automatically minimal and m g is a full factor which has w spectral gap in m finally in the appendix we give a proof of the fact that several natural notions of co amenability for an inclusion n subset m of von neumann algebras are equivalent thus closing the cycle of implications given in anantharaman delaroche s paper in 1995

compact ergodic groups of automorphisms it is shown that if g is a compact ergodic group of automorphisms on a unital c algebra a then the unique g invariant state is a trace hence if a is a von neumann algebra then it is finite and infective

generalized lie derivations on skew elements of prime algebras with involution we characterize generalized lie derivations on skew elements of prime algebras a with involution provided that a does not satisfy polynomial identities of low degree the analogous result for matrix algebras is also described

lie derivations on banach algebras abstract let d be a lie derivation on a unital complex banach algebra a then for every primitive ideal p of a except for a finite set of them which have finite codimension greater than one there exist a derivation d from a p to itself and a linear functional on a such that q p d a d a p a for all a a where q p denotes the quotient map from a onto a p moreover the preceding decomposition holds for all primitive ideals in the case where d is continuous

lie triple derivations of nest algebras abstract let n be a nest on a complex separable hilbert space h and n be the associated nest algebra in this paper we prove that every lie triple derivation from n into itself is of the form x xt tx h x i where t n and h is a linear mapping from n into c such that h a b c 0 for all a b c n

ultraproducts of von neumann algebras abstract we study several notions of ultraproducts of von neumann algebras from a unified viewpoint in particular we show that for a sigma finite von neumann algebra m the ultraproduct m introduced by ocneanu is a corner of the ultraproduct m introduced by groh and raynaud using this connection we show that the ultraproduct action of the modular automorphism group of a normal faithful state of m on the ocneanu ultraproduct is the modular automorphism group of the ultrapower state t t applying these results we obtain several properties of the ocneanu ultraproduct of type iii factors which are not present in the tracial ultraproducts for instance it turns out that the ultrapower m of a type iii0 factor is never a factor moreover we settle in the affirmative a recent problem by ueda about the connection between the relative commutant of m in m and connes asymptotic centralizer algebra m

generalized lie derivations on triangular algebras let a be a unital algebra and let m be a unitary a bimodule we consider generalized lie derivations mapping from a to m our results are applied to triangular algebras in particular to nest algebras and block upper triangular matrix algebras we prove that under certain conditions each generalized lie derivation of a triangular algebra a is the sum of a generalized derivation and a central map which vanishes on all commutators of a

commuting traces of biadditive mappings commutativity preserving mappings and lie mappings biadditive mappings b r r r where r is a prime ring with certain additional properties satisfying b x x x xb x x for all x r are characterized as an application we determine the structures of commutativity preserving mappings lie isomorphisms and lie derivations of certain prime rings

on actions of amenable groups on ii1 factors abstract given a ii 1 factor m with separable predual and a free action of a countable amenable discrete group g on m we show that the crossed product m g has property resp is mcduff when m itself has property resp is mcduff

vibration and stability of non conservative follower force systems abstract the equation which hamilton called the law of varying action is applied to obtain direct analytical solutions to stationary conservative and non conservative follower force systems with various loadings and various constraints the magnitude of the load required to produce buckling at zero frequency and or to produce flutter i e instability at non zero frequency is calculated frequency response curves and mode configurations are presented results from the direct analytical solution are compared to results from exact solutions for the few exact solutions which could be found in the literature several examples involving applied follower couples both discrete and continuous to which no published solutions could be found are also presented the paper clearly demonstrates the simplicity generality and accuracy available from hamilton s law

fullness connes χ groups and ultra products of amalgamated free products over cartan subalgebras ultra product algebras associated with amalgamated free products over cartan subalgebras are investigated as applications their connes x groups are computed in terms of ergodic theory and also we clarify what condition makes them full factors i e their inner automorphism groups become closed

a description of cp lp m rp lp m θ we give a simple explicit description of the norm in the complex interpolation space c p l p m r p l p m for any von neumann algebra m and any 1 p

generalized jordan derivation on nest algebras abstract let n be a nest on a banach space x and alg n be the associated nest algebra in this paper we prove that if there is a nontrivial element in n which is complemented in x then every additive generalized jordan derivation from alg n into itself is an additive generalized derivation moreover we give a characterization of linear generalized jordan derivations of nest algebras on complex separable hilbert spaces

lie triple derivation of the lie algebra of strictly upper triangular matrix over a commutative ring abstract let n n r be the nilpotent lie algebra consisting of all strictly upper triangular n n matrices over a 2 torsionfree commutative ring r with identity 1 in this paper we prove that any lie triple derivation of n n r can be uniquely decomposited as a sum of an inner triple derivation diagonal triple derivation central triple derivation and extremal triple derivation for n 6 in the cases 1 n 5 the results are trivial

maximal injective subalgebras of tensor products of free group factors in this article we prove the following results let l f ni be the free group factor on ni generators ni 2 and gi be one of standard generators of l f ni for 1 i n let ai be the abelian von neumann subalgebra of l f ni generated by gi then the abelian von neumann subalgebra i 1nai is a maximal injective von neumann subalgebra of i 1nl f ni when n is equal to infinity we obtain strongly stable ii1 factors or called mcduff factors that contain maximal injective abelian von neumann subalgebras

on herstein s lie map conjectures iii abstract in the two papers on herstein s lie map conjectures i and ii solutions of all of herstein s problems concerning lie isomorphisms and derivations were given under the assumption that the algebras involved were of sufficiently high dimension in the present paper we remove this restriction thereby solving herstein s problems in full generality

rigidity results for wreath product ii1 factors abstract we consider ii 1 factors of the form m g b g where either i b is a non hyperfinite ii 1 factor and g is an icc amenable group or ii b is a weakly rigid ii 1 factor and g is icc group and where g acts on g b by bernoulli shifts we prove that isomorphism of two such factors implies cocycle conjugacy of the corresponding bernoulli shift actions in particular the groups acting must be isomorphic as a consequence we can distinguish between certain classes of group von neumann algebras associated to wreath product groups

lie derivations of the skew elements of prime rings with involution abstract letrbe a prime ring with involution of the first kind and characteristic 2 3 letkdenote the skew elements ofr and letcdenote the extended centroid ofr assume that rc c 1 4 16 it is shown that any lie derivation ofkinto itself can be extended to an ordinary derivation of k counterexamples are given for the low dimension cases

hnn extensions of von neumann algebras abstract reduced hnn extensions of von neumann algebras as well as c algebras will be introduced and their modular theory factoriality and ultraproducts will be discussed in several concrete settings detailed analysis on them will be also carried out

a note on generalized derivations in banach algebras abstract in this note we characterize a complex banach algebra a admitting a generalized derivation g such that the cardinality of the spectrum g x is exactly one for all x a

the radial masa in free orthogonal quantum groups abstract we prove that the radial subalgebra in free orthogonal quantum group factors is maximal abelian and mixing and we compute the associated bimodule the proof relies on new properties of the jones wenzl projections and on an estimate of certain scalar products of coefficients of irreducible representations

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

on generalized lie derivations of lie ideals of prime algebras abstract let a be a prime algebra of characteristic not 2 with extended centroid c let r be a noncentral lie ideal of a and let b be the subalgebra of a generated by r if f d r a are linear maps satisfying that f x y f x y f y x xd y yd x for all x y r then there exist a generalized derivation g b ac c and a linear map r c such that f x g x x for all x r and r r 0 provided that a does not satisfy the standard identity of degree 18

maximal amenable subalgebras of von neumann algebras associated with hyperbolic groups we prove that for any infinite maximal amenable subgroup h in a hyperbolic group g the von neumann subalgebra lh is maximal amenable inside lg it provides many new explicit examples of maximal amenable subalgebras in ii 1 factors we also prove similar maximal amenability results for direct products of relatively hyperbolic groups and orbit equivalence relations arising from measure preserving actions of such groups

classification of type iii bernoulli crossed products abstract crossed products with noncommutative bernoulli actions were introduced by connes as the first examples of full factors of type i i i this article provides a complete classification of the factors p f n f n where f n is the free group and p is an amenable factor with an almost periodic state we show that these factors are completely classified by the rank n of the free group f n and connes s sd invariant we prove similar results for free product groups as well as for classes of generalized bernoulli actions

full factors bicentralizer flow and approximately inner automorphisms we show that a factor m is full if and only if the c algebra generated by its left and right regular representations contains the compact operators we prove that the bicentralizer flow of a type mathrm iii 1 factor is always ergodic as a consequence for any type mathrm iii 1 factor m and any lambda in 0 1 there exists an irreducible afd type mathrm iii lambda subfactor with expectation in m moreover any type mathrm iii 1 factor m which satisfies m cong m mathbin overline otimes r lambda for some lambda in 0 1 has trivial bicentralizer finally we give a counter example to the characterization of approximately inner automorphisms conjectured by connes and we prove a weaker version of this conjecture in particular we obtain a new proof of kawahigashi sutherland takesaki s result that every automorphism of the afd type mathrm iii 1 factor is approximately inner

a noncommutative extended de finetti theorem abstract the extended de finetti theorem characterizes exchangeable infinite sequences of random variables as conditionally i i d and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability our main result is a noncommutative version of this theorem in contrast to the classical result of ryll nardzewski exchangeability turns out to be stronger than spreadability for infinite sequences of noncommutative random variables out of our investigations emerges noncommutative conditional independence in terms of a von neumann algebraic structure closely related to popa s notion of commuting squares and kummerer s generalized bernoulli shifts our main result is applicable to classical probability quantum probability in particular free probability braid group representations and jones subfactors

centralizers of j subspace lattice algebras abstract let l be a j subspace lattice on a banach space and let a be a subalgebra of alg l which contains f l where f l denotes the algebra of all finite rank operators in alg l a left right centralizer of a is an additive map a a satisfying ab a b ab a b for all a b a and a centralizer of a is a both left and right centralizer in this paper we describe the general form of a centralizer of a and show that every linear local left right centralizer of a is a left right centralizer also it is proved that if a linear map f l f l satisfies p p p p p for every idempotent p in f l then is a centralizer