dilatation and order of contact for holomorphic self maps of strongly convex domains let d be a bounded strongly convex domain and let f be a holomorphic self map of d in this paper we introduce and study the dilatation alpha f of f defined if f has no fixed points in d as the usual boundary dilatation coefficient of f at its wolff point or if f has some fixed points in d as the ratio of shrinking of the kobayashi balls around a fixed point of f in particular we show that the map alpha defined as alpha f mapsto alpha f in 0 1 is lower semicontinuous among other things this allows us to study the limits of a family of holomorphic self maps of d in the case of an inner fixed point the dilatation is an intrinsic measure of the order of contact of f d to partial d finally using complex geodesics we define and study a directional dilatation which is a measure of the shrinking of the domain along a given direction again results of semicontinuity are given and applied to a family of holomorphic self maps

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

rigidity of holomorphic mappings and a new schwarz lemma at the boundary a rigidity theorem for holomorphic mappings in the nature of the uniqueness statement of the classical one variable schwarz lemma is proved at the boundary of a strongly pseudoconvex domain the result reduces to an interesting and apparently new result even in one complex dimension the theorem has a variety of geometric and analytic interpretations department of mathematics university of michigan ann arbor michigan 48109 department of mathematics box 1146 washington university in st louis st louis missouri 63130 this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 04 utc all use subject to http about jstor org terms

lie structure in semiprime superalgebras with superinvolution abstract in this paper we investigate the lie structure of the lie superalgebra k of skew elements of a semiprime associative superalgebra a with superinvolution we show that if u is a lie ideal of k then either there exists an ideal j of a such that the lie ideal j k k is nonzero and contained in u or a is a subdirect sum of a a where the image of u in a is central and a is a subdirect product of orders in simple superalgebras each at most 16 dimensional over its center

functional identities in superalgebras abstract the aim of this paper is to establish the theory of functional identities in superalgebras as an application of this theory k supercommuting maps in superalgebras are investigated

the existence of superinvolutions superinvolutions on graded associative algebras constitute a source of lie and jordan superalgebras graded versions of the classical albert and albert riehm theorems on the existence of superinvolutions are proven surprisingly the existence of superinvolutions of the first kind is a rare phenomenon as nontrivial central division superalgebras are never endowed with this kind of superinvolutions

generalized functional identities with anti automorphisms and derivations on prime rings i abstract the concept of a generalized functional identity gfi with anti automorphisms and derivations is a generalization of the notion of a generalized polynomial identity gpi with anti automorphisms and derivations in the present paper we show that either a prime ring is gpi or such gfis have only the obvious solutions our results simultaneously generalize the results of martindale rowen lanski kharchenko and chuang on gpis and a number of earlier results on gfis

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

on the lie structure of the skew elements of a simple superalgebra with superinvolution abstract we investigate the lie structure of the lie superalgebra k of skew elements of a unital simple associative superalgebra a with superinvolution over a field of characteristic not 2 it is proved that if a is more than 16 dimensional over its center z then any lie ideal u of k satisfies either u z or u k k moreover any lie ideal u of k k satisfies either u z or u k k in particular k k z k k is a simple lie superalgebra

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

the range of holomorphic maps at boundary points we prove a boundary version of the open mapping theorem for holomorphic maps between strongly pseudoconvex domains that is we prove that the local image of a holomorphic map f d rightarrow d close to a boundary regular contact point p in partial d where the jacobian is bounded away from zero along normal non tangential directions has to eventually contain every cone and more generally every region which is kobayashi asymptotic to a cone with vertex at f p

boundary behavior of infinitesimal generators in the unit ball we prove a julia wolff caratheodory type theorem for infinitesimal generators on the unit ball in n moreover we study jets expansions at the boundary and give necessary and sufficient conditions on such jets for an infinitesimal generator to generate a group of automorphisms of the ball

linear fractional maps of the unit ball a geometric study abstract we classify up to conjugation with automorphisms the linear fractional self maps of the unit ball of c n n 1 then we give some applications of these normal forms to the study of composition operators

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

boundary jets of holomorphic maps between strongly pseudoconvex domains abstract in this paper we consider jets taken at a fixed boundary point of germs of holomorphic diffeomorphisms which send one strongly pseudoconvex domain into another we completely describe possible first and second jets and conditions of extremality in terms of the chern moser normal forms of the domains

on herstein s lie map conjectures i first published in transactions american mathematical society in vol 353 no 10 pp 4235 4260 published by the american mathematical society

iteration and the solution of functional equations for functions analytic in the unit disk this paper considers the classical functional equations of schroeder f o p xf and abel f o p f 1 and related problems of fractional iteration where 9p is an analytic mapping of the open unit disk into itself the main theorem states that under very general conditions there is a linear fractional transformation 4 and a function a analytic in the disk such that a oa p and that with suitable normalization 4 and a are unique in particular the hypotheses are satisfied if 4p is a probability generating function that does not have a double zero at 0 this intertwining relates solutions of functional equations for t to solutions of the corresponding equations for d for example it follows that if 4p has no fixed points in the open disk then the solution space of f o p xf is infinite dimensional for every nonzero x although the discrete semigroup of iterates of t usually cannot be embedded in a continuous semigroup of analytic functions mapping the disk into itself we find that for each z in the disk all sufficiently large fractional iterates of p can be defined at z this enables us to find a function meromorphic in the disk that deserves to be called the infinitesimal generator of the semigroup of iterates of p if the iterates of p can be embedded in a continuous semigroup we show that the semigroup must come from the corresponding semigroup for 4 and thus be real analytic in t the proof of the main theorem is not based on the well known limit technique introduced by koenigs 1884 but rather on the construction of a riemann surface on which an extension of 9p is a bijection much work is devoted to relating characteristics of p to the particular linear fractional transformation constructed in the theorem

classification of semigroups of linear fractional maps in the unit ball we give a complete classiflcation up to conjugation of continuous semigroups of linear fractional self maps of the unit ball

lie superhomomorphisms in superalgebras with superinvolution abstract the main purpose of the present paper is to give a description of lie superhomomorphisms from the set of skew elements of a superalgebra with superinvolution into a unital superalgebra

lie isomorphisms in prime rings with involution abstract let r and r be prime rings with involutions of the first kind and with respective lie subrings of skew elements k and k furthermore assume rc c 1 4 9 16 25 64 where c is the extended centroid of r it is shown that any lie isomorphism of k onto k can be extended uniquely to an associative isomorphism of k onto k where k and k are respectively the associative subrings generated by k and k

parabolic composition operators on the ball abstract we give a classification up to automorphisms of parabolic linear fractional maps of the ball we then show that this classification is very convenient to study the geometric properties of these maps as well as the associated composition operators

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

linear preservers of zeros of matrix polynomials abstract we classify linear operators on matrices with semiring entries that preserve the zeros of multivariable matrix polynomials these matrix polynomials are defined via the adjoint operator x y xy yx as if the matrices were being considered as if over a field also we compare the results over fields with the results over semirings

cyclic behavior of linear fractional composition operators in the unit ball of c n we characterize the cyclicity and hypercyclicity of composition operators induced by linear fractional self maps of b n on the hardy space h 2 b n based on the classification of linear fractional maps given by bisi and bracci c 2007 elsevier inc all rights reserved

primitive superalgebras with superinvolution abstract our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras 5 6 10 and to classify primitive superrings with superinvolution having a minimal one sided superideal we were led to this problem by our work on finite dimensional central simple jordan superalgebras over fields of characteristic not 2 9 see also 7 of course just as symmetric elements give rise to jordan superalgebras skewsymmetric elements give rise to lie superalgebras 8 4 the results and methods are closely related to those of structure theory of associative rings and central simple associative algebras with involution 5 chap i 6 chaps ii iii 1 chap x 10 chap 2 some of the results have been announced in 13

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

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

a class of linear fractional maps of the ball and their composition operators abstract we study a class of linear fractional self maps of the ball which seems to be a good generalization of parabolic non automorphisms of the unit disk we give a normal form of these maps and use it to compute the spectrum of the composition operators induced by them we also show that these composition operators are never hypercyclic applications are given to the study of more general linear fractional transformations

homological aspects of noetherian pi hopf algebras and irreducible modules of maximal dimension abstract we prove that a noetherian hopf algebra of finite global dimension possesses further attractive homological properties at least when it satisfies a polynomial identity this applies in particular to quantized enveloping algebras and to quantized function algebras at a root of unity as well as to classical enveloping algebras in positive characteristic in all three cases we show that these algebras are auslander regular and macaulay we derive representation theoretic consequences concerning the coincidence of the non azumaya and singular loci for each of the above three classes of algebras

on additive isomorphisms of prime rings preserving polynomials we study additive isomorphisms of prime rings preserving a multilinear polynomial of degree 2 our main theorem generalizes a number of results obtained for jordan n jordan lie and lie triple isomorphisms of prime rings

on generalized functional identities on prime rings abstract in the present paper we study generalized functional identities involving multi additive functions our results simultaneously generalize martindale s theorem on prime rings with generalized polynomial identities and bresar s results on generalized functional identities of degree two

quasi identities on matrices and the cayley hamilton polynomial abstract we consider certain functional identities on the matrix algebra m n that are defined similarly as the trace identities except that the coefficients are arbitrary polynomials not necessarily those expressible by the traces the main issue is the question of whether such an identity is a consequence of the cayley hamilton identity we show that the answer is affirmative in several special cases and moreover for every such an identity p and every central polynomial c with zero constant term there exists m n such that the affirmative answer holds for c m p in general however the answer is negative we prove that there exist antisymmetric identities that do not follow from the cayley hamilton identity and give a complete description of a certain family of such identities

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

norms and spectral radii of linear fractional composition operators on the ball abstract we give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of hilbert function spaces on the ball and obtain new norm bounds analogous to the standard one variable estimates we also show that cowen s one variable spectral radius formula extends to these operators the key observation underlying these results is that every linear fractional map of the ball belongs to the schur agler class

valiron s theorem in the unit ball and spectra of composition operators abstract we prove a version of valiron s conjugacy theorem for schur class mappings of the unit ball of c n as an application we obtain a formula for the spectral radius of composition operators on the ball with schur class symbols

a proof of the muir suffridge conjecture for convex maps of the unit ball in mathbb c n c n we prove and improve the muir suffridge conjecture for holomorphic convex maps namely let f mathbb b n rightarrow mathbb c n be a univalent map from the unit ball whose image d is convex let mathcal s subset partial mathbb b n be the set of points xi such that lim z rightarrow xi vert f z vert infty then we prove that mathcal s is either empty or contains one or two points and f extends as a homeomorphism tilde f overline mathbb b n setminus mathcal s rightarrow overline d moreover mathcal s emptyset if d is bounded mathcal s has one point if d has one connected component at infty and mathcal s has two points if d has two connected components at infty and up to composition with an automorphism of the ball and renormalization f is an extension of the strip map in the plane to higher dimension

centralizing maps in prime rings with involution abstract let r be a prime ring with involution of characteristic 2 with center z skew elements k and extended centroid c theorem suppose k k 0 and k k is an additive map such that x x z for all x k then unless r is an order in a 16 dimensional central simple algebra there exists c and an additive map k c such that x x x for all x k

multiplicative lie isomorphisms between factors abstract let m n be factors if m n is a multiplicative lie isomorphism then is of the form where is a linear isomorphism or a conjugate linear isomorphism or the negative of a linear anti isomorphism or the negative of a conjugate linear anti isomorphism of m onto n and is a mapping of m into c i i c which maps commutators into zero

modular representation theory of lie algebras on etudie les representations non necessairement restreintes de l algebre universelle enveloppante u 7b g pour une algebre de lie restreinte 7b g

skew commutators and lie isomorphisms in real von neumann algebras in this paper we study skew elementsrkand their commutators in a real factorr and prove that ifrandsare real factors not of typei1andi2then derived lie algebras rk rk and sk sk are isomorphic if and only ifrandsare isomorphic

commuting traces of multiadditive mappings abstract letrbe a prime ring andmann additive mapping onrsuch that m x x x 0 for allx r if char r 0 or n then there exist mappings iofrinto the extended centroidcofrsuch that m x x i 0 n i x x n i for allx r if in addition ris not algebraic of bounded degree n then for eachithere exists ani additive mappingmiofriintocsuch that i x mi x x for allx r

infinitesimal hecke algebras of sl2 in positive characteristic abstract we describe centers of infinitesimal hecke algebra of sl 2 in positive characteristic in particular we show that these algebras are finitely generated modules over their centers and the azumaya and smooth loci of the centers coincide

on functional identities in prime rings with involution abstract let a be a prime ring with involution let s be the symmetric elements let k be the skew elements let q ml be the maximal left ring of quotients x 1 x m noncommuting variables and e i f j g k h l a m 1 q ml i j k l 1 2 m we study functional identities of the form m i 1 e i i x i m j 1 x j f j j m k 1 g k k x k m l 1 x l h l l 0 for all x 1 x m a where e i i means e i x 1 x i x m etc in case s k is not algebraic of bounded degree 2 m definitive results are obtained as an application k commuting traces of symmetric n additive maps of either s or k into q ml are characterized

the zelmanov approach to jordan homomorphisms of associative algebras abstract zelmanov s work on prime jordan algebras leads to an idempotent free version of martindale s theorem on the extension of jordan homomorphisms and derivations from the hermitian elements h r of an associative algebra of degree 2 with involution to associative homomorphisms and derivations on r the condition that j h r be of degree 2 is replaced by the intrinsic condition that j z j h a consist entirely of values of zelmanov polynomials

hyperbolic composition operators on the ball we give a classification up to automorphisms of hyperbolic linear fractional maps of the ball we then show that this classification is very convenient to study the geometric properties of these maps as well as the spectrum and the dynamics of the associated composition operators we conclude by showing how these properties can be tranfered to composition operators associated to hyperbolic self maps of the ball which are not linearfractional maps

a schwarz lemma at the boundary using the julia wolff caratheodory type condition on finite dimensional irreducible bounded symmetric domains abstract in this paper we prove a schwarz lemma at the boundary for holomorphic self mappings f of finite dimensional irreducible bounded symmetric domains without assuming the boundary regularity of f our result generalizes the previous results obtained for holomorphic self mappings f of the euclidean unit ball or of the classical cartan domains of type i and of type ii which are smooth up to the boundary