value distribution of meromorphic solutions of certain difference painleve equations abstract the borel exceptional value and the exponents of convergence of poles zeros and fixed points of finite order transcendental meromorphic solutions for difference painleve i and ii equations are estimated and the forms of rational solutions of the difference painleve ii equation and the autonomous difference painleve i equation are also given it is also proved that the non autonomous difference painleve i equation has no rational solution

idempotents in nest algebras abstract the algebraic equivalence and similarity classes of idempotents within a nest algebra alg are completely characterized we obtain necessary and sufficient conditions for two idempotents to be equivalent or similar our criterion yields examples illustrating pathology and also shows that to each equivalence class of idempotents there corresponds a dimension function from into n we complete the characterization of the algebraic equivalence classes by proving that any dimension function corresponds to an equivalence class of idempotents also to each sequence of dimension functions there corresponds a commuting sequence of idempotents a criterion is obtained for when an idempotent is similar to a subidempotent of another the mapping which sends an equivalence class or idempotent to its associated dimension function plays a role in the nest algebra theory analogous to the role played by the mapping sending a projection in a type i w algebra to its center valued trace we prove that almost commuting similar idempotents are homotopic this contrasts with the situation in certain c algebras using this we show that similar simultaneously diagonalizable idempotents are homotopic and in the continuous nest case every diagonal idempotent is homotopic to a core projection

growth and zeros of meromorphic solution of some linear difference equations abstract in this paper we study growth and zeros of linear difference equations p n z f z n p 1 z f z 1 p 0 z f z f z where f z p n z p 0 z are polynomials with f p n p 0 0 and satisfy deg p n p 0 max deg p j j 0 n 1 the corresponding homogeneous equation of the above equation is also investigated

lie isomorphisms of nest algebras on banach spaces abstract we show that a lie isomorphism between nest algebras on banach spaces can be decomposed as where is an algebraic isomorphism or a negative of an algebraic anti isomorphism and is a linear map with image in the center vanishing on each commutator

commutativity preserving linear maps and lie automorphisms of triangular matrix algebras abstract in this article we classify linear maps from the algebra t n of n upper triangular matrices into itself satisfying ab ba 0 if and only if ab ba 0 in particular we show that for n 2 any such map is either the sum of an algebra automorphism and a map into the centre or the sum of the negative of an algebra anti automorphism and a map into the centre as a consequence lie automorphisms of the algebra t n are also classified

convergence of numerical approximations to non linear continuity equations with rough force fields we prove quantitative regularity estimates for the solutions to non linear continuity equations and their discretized numerical approximations on cartesian grids when advected by a rough force field this allows us to not only recover the known optimal regularity for linear transport equations but also to obtain the convergence of a wide range of numerical schemes our proof is based on novel commutator estimates quantifying and extending to the non linear case the classical commutator approach of the theory of renormalized solutions

compactness for nonlinear continuity equations abstract we prove compactness and hence existence for solutions to a class of nonlinear transport equations the corresponding models combine the features of linear transport equations and scalar conservation laws we introduce a new method which gives quantitative compactness estimates compatible with both frameworks

extreme points in triangular uhf algebras we examine the strongly extreme point structure of the unit balls of triangular uhf algebras the semisimple triangular uhf algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal in contrast to this for the class of full nest algebras we prove a krein milman type theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points results concerning the geometry of the unit ball have a long history both in banach space theory and in the theory of operator algebras this geometry can be affiliated with structural and algebraic properties moreover differences in geometric properties can prove useful in classification problems two fundamental results are the russo dye theorem and kadison s theorem on isometries more recently there has been interest in the unit balls of nonselfadjoint operator algebras especially nest algebras 1 2 3 4 15 16 this paper concerns the unit balls of triangular uhf algebras these and the larger class of triangular af algebras are nonselfadjoint analogues of the uhf and af c algebras studied by glimm and bratteli their theory has grown rapidly cf 8 9 18 19 20 we focus on the extreme point structure and our results have a different flavor than those for nest algebras specifically we study the strongly extreme points those boundary points whose stable character with respect to approximations makes them behave well under direct limits triangular uhf algebras are direct limits of full upper triangular matrix algebras unit balls embed into unit balls in the direct limit scheme and some types of embeddings respect the extreme point structure while others do not this leads to structural differences in the limit algebras the geometric structures of the unit balls of different triangular uhf algebras can be very dissimilar the convex hull of the strongly extreme points even without closure always contains the unit ball of the diagonal theorem 7 shows that the two coincide if and only if the algebra is semisimple this is a characterization of a purely geometric property in terms of a purely algebraic one in contrast to received by the editors january 11 1996 and in revised form march 28 1996 1991 mathematics subject classification primary 47d25 46k50 46b20

growth and integrability in the dynamics of mappings the growth of some numerical characteristics of the mappings under their iterations in the context of the general problem of integrability is discussed in the general case such characteristics as complexity by arnold or the number of the different images for the multiple valued mappings are growing exponentially it is shown that the integrability is closely related with thepolynomial growth the analogies with quantum integrable systems are discussed

relationships between characteristic functions of δnf and f abstract in this paper we obtain the accurate relationships between the characteristic functions of a finite order meromorphic function f z and its forward differences n f z where f z has two borel exceptional values

commutators and images of noncommutative polynomials abstract let a be an algebra and let f be a nonconstant noncommutative polynomial in the first part of the paper we consider the relationship between a a the linear span of commutators in a and span f a the linear span of the image of f in a in particular we show that a a a implies span f a a in the second part we establish some waring type results for images of polynomials for example we show that if c is a commutative unital algebra over a field f of characteristic 0 a is the matrix algebra m n c and the polynomial f is neither an identity nor a central polynomial of m n f then every commutator in a can be written as a difference of two elements each of which is a sum of 7788 elements from f a if c f is an algebraically closed field then 4 elements suffice similar results are obtained for some other algebras in particular for the algebra b h of all bounded linear operators on a hilbert space h

on properties of meromorphic solutions for difference equations concerning gamma function abstract in this paper we mainly consider the properties of differences of meromorphic solutions for the difference equation a 1 z f z 1 a 0 z f z 0 concerning a gamma function where a 1 z and a 0 z are nonzero polynomials by these properties we deduce that a gamma function satisfies that for every n n n z z 0 n z has only n zeros z z z j z 1 j 0 1 n 1 z 1 z 1 n 1 z and 1 z have same zeros at most except n exceptional zeros where g denotes the order of growth of a meromorphic function g and g and g denote the exponents of convergence of fixed points and zeros of g respectively

renormalized solutions to the vlasov equation with coefficients of bounded variation we prove that weak bounded solutions to the vlasov equation with bv coefficients have the renormalization property and we show that when the renormalization property holds for a general transport equation it also holds for only lipschitz nonlinearities

global existence of weak solutions for compresssible navier stokes equations thermodynamically unstable pressure and anisotropic viscous stress tensor we prove global existence of appropriate weak solutions for the compressible navier stokes equations for more general stress tensor than those covered by p l lions and e feireisl s theory more precisely we focus on more general pressure laws which are not thermodynamically stable we are also able to handle some anisotropy in the viscous stress tensor to give answers to these two longstanding problems we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates this requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation these two cases open the theory to important physical applications for instance to describe solar events virial pressure law geophysical flows eddy viscosity or biological situations anisotropy

convergence of the mac scheme for the compressible stokes equations we prove in this paper the convergence of the marker and cell mac scheme for the discretization of the steady state compressible stokes equations on two or three dimensional cartesian grids the existence of a solution to the scheme is proven followed by estimates on approximate solutions which yield the convergence of the approximate solutions up to a subsequence and in an appropriate sense we then prove that the limit of the approximate solutions satisfies the mass and momentum balance equations as well as the equation of state which is the main difficulty of this study

bilinear trilinear forms and exact solution of certain fourth order integrable difference equations a systematic investigation of finding bilinear or trilinear representations of fourth order autonomous ordinary difference equation x n 4 f x n x n 1 x n 2 x n 3 or xn 4 f xn xn 1 xn 2 xn 3 is made as an illustration we consider fourth order symplectic integrable difference equations reported by capel and sahadevan physica a 289 86 2001 and derived their bilinear or trilinear forms also it is shown that the obtained bilinear representations admit exact solution of rational form

weak solutions for some compressible multicomponent fluid models the principle purpose of this work is to investigate a viscous version of a simple but still realistic bi fluid model described in bresch et al in giga novotn eds handbook of mathematical analysis in mechanics of viscous fluids 2018 whose non viscous version is derived from physical considerations in ishii and hibiki thermo fluid dynamics of two phase flow springer berlin 2006 as a particular sample of a multifluid model with algebraic closure the goal is to show the existence of weak solutions for large initial data on an arbitrarily large time interval we achieve this goal by transforming the model to a transformed two densities system which resembles the compressible navier stokes equations with however two continuity equations and a momentum equation endowed with the pressure of a complicated structure dependent on two variable densities the new transformed two densities system is then solved by an adaptation of the lions feireisl approach for solving compressible navier stokes equation completed with several observations related to the diperna lions transport theory inspired by maltese et al j differ equ 261 4448 4485 2016 and vasseur et al j math pures appl 125 247 282 2019 we also explain how these techniques can be generalized to a model of mixtures with more than two species this is the first result on the existence of weak solutions for any realistic multifluid system

the second main theorem for small functions and related problems we shall establish the following three results in more general forms 1 the second main theorem for small functions let f be a meromorphic function on the complex plane c let a1 aq be distinct meromorphic functions on c assume that ai are small with respect to f i e t r a 0 corollary 1 here as usual in nevanlinna theory the terms t r f and n r ai f denote for the characteristic function and the truncated counting function respectively 2 application to functional equations let kc be the field of meromorphic functions on c for a function r 0 r put k c a kc t r a o r which is a subfield of kc then the following holds let f x y k c x y be a polynomial in two variables over k c assume that the curve f x y 0 over k c has genus greater than one if 1 2 kc satisfy the functional equation f 1 2 0 then both 1 and 2 are contained in k c corollary 2 3 height inequality for curves over function fields let k be a function field of one variable over c let x be a smooth projective curve over k let d x be a reduced divisor let l be an ample line bundle on x and let e 0 then we have hk kx d p n 1 k s d p dk p ehk l p oe 1 for all p x k d theorem 5 here the notations are introduced in v1 v3 see also section 9 our proof uses ahlfors theory of covering surfaces and the geometry of the moduli space of q pointed stable curves of genus 0

meromorphic solutions of difference equations integrability and the discrete painleve equations the painlev e property is closely connected to differential equations that are integrable via related iso monodromy problems many apparently integrable discrete analogues of the painlev e equations have appeared in the literature the existence of sufficiently many finite order meromorphic solutions appears to be a good analogue of the painlev e property for discrete equations in which the independent variable is taken to be complex a general introduction to nevanlinna theory is presented together with an overview of recent applications to meromorphic solutions of difference equations and the difference and q difference operators new results are presented concerning equations of the form w z 1 w z 1 r z w where r is rational in w with meromorphic coefficients

existence of finite order meromorphic solutions as a detector of integrability in difference equations abstract the existence of sufficiently many finite order in the sense of nevanlinna meromorphic solutions of a difference equation appears to be a good indicator of integrability it is shown that out of a large class of second order difference equations the only equation that can admit a sufficiently general finite order meromorphic solution is the difference painleve ii equation the proof given relies on estimates obtained by arguments related to singularity confinement the existence of meromorphic solutions of a general class of first order difference equations is also proven by a simple method based on banach s fixed point theorem

lie isomorphisms of reflexive algebras a lie isomorphism between algebras is called trivial if where is an algebraic isomorphism or a negative of an algebraic anti isomorphism and is a linear map with image in the center vanishing on each commutator in this paper we investigate the conditions for the triviality of lie isomorphisms from reflexive algebras with completely distributive and commutative lattices cdcsl in particular we prove that a lie isomorphism between irreducible cdcsl algebras is trivial if and only if it preserves i idempotent operators the sum of an idempotent and a scalar multiple of the identity in both directions we also prove the triviality of each lie isomorphism from a cdcsl algebra onto a csl algebra which has a comparable invariant projection with rank and corank not one some examples of lie isomorphisms are presented to show the sharpness of the conditions

lie ideals from pure algebra to c algebras how does the associative structure of the algebra a e ect the lie structure of a in particular is it possible to describe lie ideals of a through associative ideals of a this and related questions such as the link between lie ideals and conjugate invariant subspaces of unital algebras have been an active area of research for more than 50 years they have been studied in pure algebra see e g a bfm h1 h2 h3 jr lm mm1 mm2 mu and more or less independently also in functional analysis particularly in operator algebras see e g bm cy fm fr fms fn hms hp ma mamu ms mi to one of the goals of this paper is to glue these two areas that is we will apply purely algebraic results derived in the first part of the paper to the second part dealing with banach algebras especially with w algebras and c algebras

a convergent fem dg method for the compressible navier stokes equations this paper presents a new numerical method for the compressible navier stokes equations governing the flow of an ideal isentropic gas to approximate the continuity equation the method utilizes a discontinuous galerkin discretization on piecewise constants and a basic upwind flux for the momentum equation the method is a new combined discontinuous galerkin and finite element method approximating the velocity in the crouzeix raviart finite element space while the diffusion operator is discretized in a standard fashion the convection and time derivative are discretized using discontinuous galerkin on the element average velocity and a lax friedrich type flux our main result is convergence of the method to a global weak solution as discretization parameters go to zero the convergence analysis constitutes a numerical version of the existence analysis of lions and feireisl

linear maps preserving commutativity abstract commutativity preserving maps on the real space of all real symmetric or complex self adjoint matrices are characterized related results are given for adjoint preserving maps defined on all n n matrices these results are extended to infinite dimensions in the case of invertible maps

on lie and associative algebras containing inner derivations abstract we describe subalgebras of the lie algebra gl n 2 that contain all inner derivations of a m n f where n 5 and f is an algebraically closed field of characteristic 0 in a more general context where a is a prime algebra satisfying certain technical restrictions we establish a density theorem for the associative algebra generated by all inner derivations of a

on the value distribution of some difference polynomials abstract in this paper we continue to investigate the value distribution of some difference polynomials which can be considered as difference counterparts of some classic results of hayman

closed form expressions for integrals of mkdv and sine gordon maps we present closed form expressions for approximately n integrals of 2n dimensional maps the maps are obtained by travelling wave reductions of the modified korteweg de vries equation and of the sine gordon equation respectively we provide the integrating factors corresponding to the integrals moreover we show how the integrals and the integrating factors relate to the staircase method

algebraic isomorphisms of limit algebras we prove that algebraic isomorphisms between limit algebras are automatically continuous and consider the consequences of this result in particular we give partial solutions to a conjecture and an open problem by power as a further consequence we describe epimorphisms between various classes of limit algebras in this paper we study automatic continuity for limit algebras automatic continuity involves algebraic conditions on a linear operator from one banach algebra into another that guarantee the norm continuity of the operator this is a generalization via the open mapping theorem of the uniqueness of norms problem recall that a banach algebra a is said to have a unique banach algebra topology if any two complete algebra norms on a are equivalent so that the norm topology determined by a banach algebra is unique uniqueness of norms automatic continuity and related questions have played an important and long standing role in the theory of banach algebras 6 29 28 10 11 2 limit algebras whose theory has grown rapidly in recent years are the nonselfadjoint analogues of uhf and af c algebras we first prove that algebraic isomorphisms between limit algebras are automatically continuous theorem 1 4 this proof uses the ideal theory of limit algebras as well as key results from the theory of automatic continuity for banach algebras combining this with 23 theorem 8 3 verifies power s conjecture that the c envelope of a limit algebra is an invariant for purely algebraic isomorphisms for limits of finite dimensional nest algebras and in particular for all triangular limit algebras corollary 1 6 in 5 the first two authors studied triangular limit algebras in terms of their lattices of ideals by combining automatic continuity with this work we show that within the class of algebras generated by their order preserving normalizers see below for definitions algebraically isomorphic algebras are isometrically isomorphic theorem 2 5 this shows that the spectrum or fundamental relation 20 a topological binary relation which provides coordinates for limit algebras and is a useful tool in classifications is a complete algebraic isomorphism invariant for this class corollary 2 6 in recent work the second two authors studied primitivity for limit algebras 9 showing that a variety of limit algebras are primitive these results together with automatic continuity give descriptions of epimorphisms between various classes of limit algebras namely lexicographic algebras theorem 3 2 and z analytic algebras theorem 3 3 received by the editors april 6 1998 and in revised form october 7 1999 2000 mathematics subject classification primary 47d25 46k50 46h40 research partially supported by an nsf grant 2000 american mathematical society

the lattice of ideals of a triangular af algebra we study triangular af taf algebras in terms of their lattices of closed two sided ideals not isometrically isomorphic taf algebras can have isomorphic lattices of ideals indeed there is an uncountable family of pairwise non isomorphic algebras all with isomorphic lattices of ideals in the positive direction if a and b are strongly maximal taf algebras with isomorphic lattices of ideals then there is a bijective isometry between the subalgebras of a and b generated by their order preserving normalizers this bijective isometry is the sum of an algebra isomorphism and an anti isomorphism using this we show that if the taf algebras are generated by their order preserving normalizers and are triangular subalgebras of primitive c algebras then the lattices of ideals are isomorphic if and only if the algebras are either isometrically isomorphic or anti isomorphic finally we use complete distributivity to show that there are taf algebras whose 0 lattices of ideals can not arise from taf algebras generated by their order preserving 8 normalizers our techniques rely on constructing a topological binary relation based on the lattice of ideals this relation is closely connected to the spectrum or fundamental relation also a topological binary relation of the taf algebra

elementary exact calculations of degree growth and entropy for discrete equations second order discrete equations are studied over the field of rational functions c z where z is a variable not appearing in the equation the exact degree of each iterate as a function of z can b

singularity complexity and quasi integrability of rational mappings we investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models by exploiting their nature of birational transformations of projective spaces we give an algorithmic analysis of the structure of invariants of such mappings we discuss some characteristic conditions for their quasi integrability and in particular its links with their singularities in the 2 plane finally we describe some of their propertiesqua dynamical systems making contact with arnol d s notion of complexity and exemplify remarkable behaviours

the orthogonal lie algebra of operators ideals and derivations abstract we study in this paper the infinite dimensional orthogonal lie algebra o c which consists of all bounded linear operators t on a separable infinite dimensional complex hilbert space h satisfying c t c t where c is a conjugation on h by employing results from the theory of complex symmetric operators and skew symmetric operators we determine the lie ideals of o c and their dual spaces we study derivations of o c and determine their spectra these results complete some results of p de la harpe and provide interesting contrasts between o c and the algebra b h of all bounded linear operators on h

herstein s lie theory revisited an associative ring r becomes a jordan ring r under x 0 y xy yx and a lie ring r under x y xy yx in case r has an involution i e an antiautomorphism of period 1 or 2 then the set of symmetric elements s s e r 1 s s is a jordan subring of r and the set of skew elements k ker 1 k k is a lie subring of rp in the early 1950s herstein initiated a study of the jordan and lie ideals of r s and k in case that r was a simple associative ring either without or with an involution in the ensuring years his work has been generalized in various directions on the one hand to the setting of prime and semiprime rings and on the other hand to invariance conditions other than that given by ideals besides herstein himself we mention lanski as having been a major force in this program their influence is certainly felt in the present paper we have taken the liberty of using various arguments without making specific mention from their papers notably 6 and s other important contributions in this area have also been made by baxter chacron erickson montgomery osborn streb and others part of our motivation in writing this paper is to obtain the lie ideal theory for semiprime rings with involution by a somewhat different approach from the self contained elementary very clever methods embodied in the original style of herstein let us describe very briefly the spirit of our approach for r a ring with involution and 1 any ideal i e an ideal invariant under in k k is always a lie ideal of k which we shall call a standard lie ideal of k a

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

nilpotency and generalized lie ideals the motivation for this paper arises from two desires the first is to generalize in a natural way the notion of a lie inner ideal of an associative ring originally studied by benkart cl we recall that a lie inner idea of a ring r is an additive subgroup v such that v v r c v the second is to find a lie type notion that will not only include lie ideals but will also include in an appropriate sense nilpotent associative subrings since these sometimes arise in a lie setting e g strictly triangular matrices the concept we are looking for appears to be that of a generalized lie ideal which we proceed to define after making a few remarks concerning notation let v and w be subsets of a ring r we define i w inductively as follows v w v w vcm l w v vcm w the notation i will mean v mil v v will have its usual associative meaning

lie isomorphisms of nest algebras abstract in this paper we characterize linear maps between two nest algebras t n and t m which satisfy the property that ab ba a b b a for all a b t n in particular it is shown that such isomorphisms only exist if n is similar to m or m

primitive triangular uhf algebras abstract we prove that a large class of triangular uhf algebras are primitive we use two avenues to obtain our results a direct approach in which we explicitly construct a faithful algebraically irreducible representation of the algebra on a separable hilbert space as well as an indirect algebraic approach which utilizes the prime ideal structure of the algebra using these results we completely characterize the primitive ideal spaces of all lexicographic algebras an ideal there is primitive if and only if it is closed prime specializing on the algebras a q we obtain a complete classification of their algebraic isomorphisms and epimorphisms through the use of a new invariant involving the primitive ideal space finally we characterize the primitive ideal spaces of z analytic and order preserving algebras and obtain information about their epimorphisms

exponential self similar mixing by incompressible flows we study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions the scalar solves the continuity equation with a divergence free velocity field which satisfies a bound in the sobolev space ws p where s 0 and 1 p the mixing properties are given in terms of a characteristic length scale called the mixing scale we consider two notions of mixing scale one functional expressed in terms of the homogeneous sobolev norm h 1 the other geometric related to rearrangements of sets we study rates of decay in time of both scales under self similar mixing for the case s 1 and 1 p including the case of lipschitz continuous velocities and the case of physical interest of enstrophy constrained flows we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound established in previous works on the time decay of both scales we also present several consequences for the geometry of regular lagrangian flows associated to sobolev velocity fields

uniqueness in the cauchy problem for transport in r2 and r1 2 abstract suppose that x x 1 x 2 is a planar vector field with bounded coefficients and bounded divergence suppose in addition that x preserves a volume with lipschitz continuous density we prove that there is uniqueness in the cauchy problem for the transport operator t x and also uniqueness in the cauchy problem for x at noncharacteristic hypersurfaces

some properties of meromorphic solutions of q difference equations abstract we investigate the growth of transcendental meromorphic solutions of some complex q difference equations and find lower bounds for nevanlinna lower order for meromorphic solutions of such equations we also obtain a q difference version of tumura clunie theorem

maps preserving products xy yx on von neumann algebras nnsf of china 11071201 ynsf of china 11001230 fundamental research funds for the central universities 2010121001 ynsf of fujian 2008f3013

a convergent finite element finite volume scheme for the compressible stokes problem part i the isothermal case in this paper we propose a discretization for the nonlinearized compressible stokes problem with a linear equation of state rho p based on crouzeix raviart elements the approximation of the momentum balance is obtained by usual finite element techniques since the pressure is piecewise constant the discrete mass balance takes the form of a finite volume scheme in which we introduce an upwinding of the density together with two additional stabilization terms we prove em a priori estimates for the discrete solution which yields its existence by a topological degree argument and then the convergence of the scheme to a solution of the continuous problem

singularity confinement and chaos in discrete systems we present a number of second order maps which pass the singularity confinement test commonly used to identify integrable discrete systems but which nevertheless are non integrable as a more sensitive integrability test we propose the analysis of the complexity algebraic entropy of the map using the growth of the degree of its iterates integrability is associated with polynomial growth while the generic growth is exponential for chaotic systems

lie ideals in triangular operator algebras we study lie ideals in two classes of triangular operator algebras nest algebras and triangular uhf algebras our main results show that if 2 is a closed lie ideal of the triangular operator algebra a then there exist a closed associative ideal ic and a closed subalgebra or of the diagonal a ni a so that k c 2 c ic oc introduction let a be an associative complex algebra under the lie multiplication x y xy yx a becomes a lie algebra a lie ideal in a is a linear manifold z in a for which a k c for every a e a and k c 2 in many instances there is a close connection between the lie ideal structure and the associative ideal structure of a this connection has been investigated for prime rings in 6 in 3 for b 5 the set of bounded operators on a hilbert space si and in 10 for certain von neumann algebras see also 9 4 11 in this paper we pursue this line of investigation for two classes of triangular operator algebras namely nest algebras anld triangular uhf algebras the authors would like to thank frank a zorzitto for many helpful conversations 1 weakly closed lie ideals in nest algebras recall that a nest jk on a hilbert space si is a chain of closed subspaces of si which is closed under the operations of arbitrary intersections and closed linear spans and which includes o and s5 the nest algebra t kj is the algebra of all operators on se leaving every member of jk invariant this is always closed in the weak operator topology the diagonal d kj of a nest algebra t jk is the von neumann subalgebra 7 k n t k if e f e kv with e f then f e is called an interval of the nest the nonzero minimal intervals are called atoms a nest is atomic if the atoms of the nest span 55 we refer the reader to 1 for more information on nest algebras our main result theorem 12 shows that for every weakly closed lie ideal z in 7 jk there exist a corresponding weakly closed associative ideal ic and a von neumann subalgebra sk of o a such that

on the growth of logarithmic differences difference quotients and logarithmic derivatives of meromorphic functions a crucial ingredient in the recent discovery by ablowitz halburd herbst and korhonen 2000 2007 that a connection exists between discrete painleve equations and finite order nevanlinna theory is an estimate of the integrated average of log f z 1 f z on z r we obtained essentially the same estimate in our previous paper 2008 independent of halburd et al 2006 we continue our study in this paper by establishing complete asymptotic relations amongst the logarithmic differences difference quotients and logarithmic derivatives for finite order meromorphic functions in addition to the potential applications of our new estimates in integrable systems they are also of independent interest in particular our findings show that there are marked differences between the growth of meromorphic functions with nevanlinna order less than and greater than one we have established a difference analogue of the classical wiman valiron type estimates for meromorphic functions with order less than one which allow us to prove that all entire solutions of linear difference equations with polynomial coefficients of order less than one must have positive rational order of growth we have also established that any entire solution to a first order algebraic difference equation with polynomial coefficients must have a positive order of growth which is a difference analogue of a classical result of polya

estimates and regularity results for the diperna lions flow in this paper we derive new simple estimates for ordinary differential equations with sobolev coefficients these estimates not only allow to recover some old and recent results in a simple direct way but they also have some new interesting corollaries

banach lie algebras with lie subalgebras of finite codimension their invariant subspaces and lie ideals the paper studies the existence of closed invariant subspaces for a lie algebra l of bounded operators on an infinite dimensional banach space x it is assumed that l contains a lie subalgebra l0 that has a non trivial closed invariant subspace in x of finite codimension or dimension it is proved that l itself has a non trivial closed invariant subspace in the following two cases 1 l0 has finite codimension in l and there are lie subalgebras l0 l0 l1 lp l such that li 1 li li li 1 for all i 2 l0 is a lie ideal of l and dim l0 these results are applied to the problem of the existence of non trivial closed lie ideals and closed characteristic lie ideals in an infinite dimensional banach lie algebra l that contains a non trivial closed lie subalgebra of finite codimension

meromorphic solutions of difference painleve equations we show that under certain conditions some difference painleve equations have nontrivial meromorphic solutions in the whole complex plane these meromorphic solutions are obtained by analytic continuation of asymptotic solutions given in sectors of zero opening angle the existence of these asymptotic solutions is shown by using fundamental matrix solutions of the associated linear systems with double unit characteristic roots and with coefficients expressed by asymptotic series in fractional powers

nest algebras and similarity transformations in recent years the theory of algebras of operators on hilbert space has been stimulated by developments in the theory of quasitriangularity andersen 1 has shown that up to unitary equivalence there is only one continuous quasitrianguilar algebra we use this to provide the following answer to a question posed by j r ringrose approximately 20 years ago similar continuous nests on separable hilbert space can fail to be unitarily equivalent theorem 2 2 a consequence is the existence of a nonhyperintransitive compact operator corollary 2 3 which answers a question of kadison and singer 12 and of gohberg and krein 11 we extend our initial theorem to show that arbitrary continuous nests are similar theorem 2 10 and that every maximal nest is similar to a multiplicity one nest theorem 2 11 a consequence is that every compact operator is similar to a hyperintransitive compact operator corollary 2 12 the similarity transformation can be induced by an arbitrarily small compact perturbation of a unitary operator the methods of section 2 apply only to the continuous parts of nests for general results the atomic core part must be dealt with in section 3 different methods are developed for this purpose again utilizing andersen s results these are used in section 4 to prove that a complete nest x admits an arveson factorization for every positive invertible operator if and only if x is countable as a family of subspaces theorem 4 7 a consequence is that if x is an uncountable nest with atomic core then some similarity transformation of x has a continuous part this could not be deduced from section 2 these methods also yield a weak factorization result which concludes the paper it should be noted that a negative resolution to the ringrose question was conjectured in recent years by several mathematicians including w arveson and j ringrose also many of the results presented in this paper were announced in an a m s bulletin article 16 finally we wish to thank the referee for suggesting that the original manuscript could be condensed and improved

local lie derivations of nest algebras abstract let n be a nest on a hilbert space h and alg n be the associated nest algebra we prove that every local lie derivation from alg n into b h is a lie derivation

nevanlinna theory for the q difference operator and meromorphic solutions of q difference equations it is shown that if f is a meromorphic function of order zero and q in mathbb c then begin equation label abstid m bigg r frac f qz f z bigg o t r f tag ddag end equation for all r on a set of logarithmic density 1 the remainder of the paper consists of applications of identity eqref abstid to the study of value distribution of zero order meromorphic functions and in particular zero order meromorphic solutions of q difference equations the results obtained include q shift analogues of the second main theorem of nevanlinna theory picard s theorem and clunie and mohon ko lemmas

automorphisms of the lie algebra of upper triangular matrices over a connected commutative ring abstract let r be a non trivial commutative ring having no idempotents except 0 and 1 denote by t the lie algebra over r consisting of all upper triangular n by n matrices over r we give an explicit description of the automorphism group of this lie algebra

lie gradings on associative algebras abstract in this paper we apply the method of functional identities to the study of group gradings by an abelian group g on simple lie algebras under very mild restrictions on the grading group or the base field of coefficients

ideals in some continuous nonselfadjoint crossed product algebras abstract let y t be a locally compact dynamical system where the t denotes a continuous one parameter semigroup of maps on y when each t is a homeomorphism a nonselfadjoint crossed product algebra is defined as the subalgebra of the c crossed product c 0 y r supported on t 0 when each t is only continuous the crossed product c 0 y r can still be defined the ideal structure of such an algebra is determined in the case where the semigroup action is the suspension of a discrete free action on a smaller space x a generalization of effros hahn is given whereby one may find a meet irreducible ideal over any arc closure in y the meet irreducible ideals form a topological space in the hull kernel topology and there is a one to one correspondence between closed sets in this space and closed ideals in the algebra a subset of this space is homeomorphic to the space of finite arcs in the subarc topology the irrational flow algebra is considered as a special case