a note on α β derivations abstract we show that every multiplicative derivation of a ring r is additive if there exists an idempotent e e 0 1 in r satisfying the conditions c1 c3 c1 e r x 0 implies x 0 c2 e x e r 1 e 0 implies e x e 0 c3 x r 0 implies x 0 in particular every multiplicative derivation of a prime ring with a nontrivial idempotent is additive as applications we could decompose a multiplicative derivation of the algebra m n c of all the n n complex matrices into a sum of an inner derivation and an derivation on m n c given by an additive derivation f on c

symbolic computation of fisher information matrices for parametrized state space systems the asymptotic fisher information matrix fim has several applications in linear systems theory and statistical parameter estimation it occurs in relation to the cramer rao lower bound for the covariance of unbiased estimators it is explicitly used in the method of scoring and it determines the asymptotic convergence properties of various system identification methods it defines the fisher metric on manifolds of systems and it can be used to analyze questions on identifiability of parametrized model classes for many of these applications exact symbolic computation of the fim can be of great use in this paper two different methods are described for the symbolic computation of the asymptotic fim the first method applies to parametrized mimo state space systems driven by stationary gaussian white noise and proceeds via the solution of discrete time lyapunov and sylvester equations for which a method based on faddeev sequences is used this approach also leads to new short proofs of certain well known results on the structure of the fim for siso arma systems the second method applies to parametrized siso state space systems and uses an extended faddeev algorithm for both algorithms the concept of a faddeev reachability matrix and the solution of discrete time sylvester equations in controller companion form are central issues the methods are illustrated by two worked examples the first concerns three different parametrizations of the class of stable ar n systems the second concerns a model for an industrial mixing process in which the value of exact computation to answer identifiability questions becomes particularly clear

nonlinear maps preserving jordan triple η products let 1 be a non zero complex number and let be a not necessarily linear bijection between two von neumann algebras one of which has no central abelian projections satisfying i i and preserving the jordan triple product it is showed that is a linear isomorphism if is not real and is the sum of a linear isomorphism and a conjugate linear isomorphism if is real

nonlinear lie derivations of triangular algebras in this paper we prove that every nonlinear lie derivation of triangular algebras is the sum of an additive derivation and a map into its center sending commutators to zero

ring isomorphisms and linear or additive maps preserving zero products on nest algebras it is shown that every ring isomorphism between norm closed standard subalgebras of nest algebras acting on infinite dimensional banach spaces is either a spatial isomorphism or a spatial conjugate isomorphism this is then used to characterize the linear or additive maps between nest algebras which preserve zero products

additivity of jordan maps on standard jordan operator algebras abstract let a be a standard jordan operator algebra on a hilbert space of dimension 1 and b be an arbitrary jordan algebra in this note we prove that if a bijection a b satisfies a b a b for all a b a where is the special jordan product on a then is additive

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

a second multivariable normal form for model reduction of discrete time systems the normal form derived by mansour i for single input single output time invariant linear discrete systems will be extended to the multivariable case an algorithm will be used to achieve simple computation of this form starting with the luenberger first canonical form the construction of this form will be illustrated by examples applied to model reduction of multivariable discrete time systems

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

multiplicative mappings of operator algebras nest algebras are the natural analogues of upper triangular matix algebras in an infinite dimensional hilbert space in this paper we study multiplicative isomorphisms of subalgebras of nest algebras which contain all finite rank operators but might contain no idempotents we prove that such multiplicative mappings are automatically additive and linear or conjugate linear

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

jordan triple maps abstract let a be a standard operator algebra on a banach space of dimension 1 and b be an algebra over the field of rational numbers let k be a non zero rational number in this note we prove that if a bijection a b satisfies kaba k a b a for all a b a or k abc cba k a b c c b a for all a b c a then is additive

on model reduction of discrete time systems abstract in this paper further justification of model reduction by badreddin mansour s method is presented in particular connections between polynomial root location properties coefficient properties and schur cohn coefficient properties are established lattice realizations of a discrete system and its reduced model are given which illustrate certain relationships between the original model and its reduced form these relationships give insight into the validity of the method of reduction and offer insight on the order of approximation

multiplicative jordan triple isomorphisms on the self adjoint elements of von neumann algebras abstract in this paper we consider multiplicative jordan triple isomorphisms between the sets of self adjoint elements respectively the sets of positive elements of von neumann algebras these transformations are the bijective maps which satisfy the equality aba a b a on their domains we show that all those transformations originate from linear algebra isomorphisms and linear algebra antiisomorphisms in the case when the underlying von neumann algebras do not have commutative direct summands an application of our results concerning non linear maps which preserve the absolute value of products is also presented

commuting traces and commutativity preserving maps on triangular algebras abstract let a be a triangular algebra the problem of describing the form of a bilinear map b a a a satisfying b x x x x b x x for all x a is considered as an application commutativity preserving maps and lie isomorphisms of certain triangular algebras e g upper triangular matrix algebras and nest algebras are determined

additivity of jordan maps on jordan algebras abstract let a and b be two jordan algebras in this paper we investigate the additivity of maps from a onto b that are bijective and satisfy a b a b for all a b a if a contains an idempotent which satisfies some conditions then is additive this result generalizes all results about additivity of jordan maps in 1 3 9 11

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 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

on gaussian channels with feedback under expected power constraints and with non vanishing error probabilities in this paper we consider single and multi user gaussian channels with feedback under expected power constraints and with non vanishing error probabilities in the first of two contributions we study asymptotic expansions for the additive white gaussian noise awgn channel with feedback under the average error probability formalism by drawing ideas from gallager and nakiboglu s work for the direct part and the meta converse for the converse part we establish the varepsilon capacity and show that it depends on varepsilon in general and so the strong converse fails to hold furthermore we provide bounds on the second order term in the asymptotic expansion we show that for any positive integer l the second order term is bounded between a term proportional to ln l n where ln l cdot is the l fold nested logarithm function and a term proportional to n ln n 1 2 where n is the blocklength the lower bound on the second order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available in our second contribution we establish the varepsilon capacity region for the awgn multiple access channel with feedback under the expected power constraint by combining ideas from hypothesis testing information spectrum analysis ozarow s coding scheme and power control

variations on a theme by schalkwijk and kailath schalkwijk and kailath 1966 developed a class of block codes for gaussian channels with ideal feedback for which the probability of decoding error decreases as a second order exponent in block length for rates below capacity this well known but surprising result is explained and simply derived here in terms of a result by elias 1956 concerning the minimum mean square distortion achievable in transmitting a single gaussian random variable over multiple uses of the same gaussian channel a simple modification of the schalkwijk kailath scheme is then shown to have an error probability that decreases with an exponential order which is linearly increasing with block length in the infinite bandwidth limit this scheme produces zero error probability using bounded expected energy at all rates below capacity a lower bound on error probability for the finite bandwidth case is then derived in which the error probability decreases with an exponential order which is linearly increasing in block length at the same rate as the upper bound

ring isomorphisms and pentagon subspace lattices abstract if k l and m are closed subspaces of a banach space x satisfying k m 0 k l x and l m then p 0 k l m x is called a pentagon subspace lattice on x let p i be a pentagon subspace lattice on a complex banach space x i for i 1 2 then every ring isomorphism from alg p 1 onto alg p 2 is a quasi spatially induced linear or conjugate linear algebra isomorphism

additivity of multiplicative maps on triangular rings in this paper we shall give a unified technique in the discussion of the additivity of n multiplicative automorphisms n multiplicative derivations n elementary surjective maps and jordan multiplicative surjective maps on triangular rings

the structure of lie derivations on c algebras we prove that every lie derivation on a c algebra is in standard form that is it can be

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

jordan maps of nest algebras abstract in this paper we prove that a bijective map from a a standard subalgebra of a nest algebra on a hilbert space onto an algebra that satisfies r ab ba r a b b a a b a where r is a fixed nonzero rational number is additive

lie derivable maps on b x abstract let x be a banach space of dimension greater than 1 we prove that if a map b x b x satisfies a b a b a b for any a b b x then d where d is an additive derivation of b x and the map b x f i vanishes at commutators a b

additivity of jordan maps on standard operator algebras abstract in this paper we prove that a bijective map form a a standard operator algebra on a banach space of dimension 1 onto a ring that satisfies ab ba a b b a a b a is additive

maps on matrix spaces it is well known that every automorphism of the full matrix algebra is inner we give a short proof of this statement and discuss several extensions of this theorem including structural results for multiplicative maps on matrix algebras characterizations of monotone and orthogonality preserving maps on idempotent matrices some nonlinear preserver results and some recent theorems concerning geometry of matrices we show that all these topics are closely related and point out the connections with physics and geometry several open problems are posed

elementary maps on nest algebras abstract let a 1 a 2 be algebras and let m a 1 a 2 m a 2 a 1 be maps an elementary map of a 1 a 2 is an ordered pair m m such that m a m b c m a b m c m b m a d m b a m d for all a c a 1 b d a 2 in this paper the general form of surjective elementary maps on standard subalgebras of nest algebras is described in particular such maps are automatically additive

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

reduced order iir approximation to fir digital filters an algorithm for designing an infinite impulse response iir stable filter using a finite impulse response fir given filter with the objective of reducing the delay and order is described the design is in the time domain using the least squares inverse algorithm which is briefly described in this method the numerator of the approximated filter is part of the fir filter itself and no calculations and minimization are needed to find the numerator coefficients except finding the fir roots an error analysis between the given fir and approximated iir filters is provided this error analysis enables the designer to fix a design parameter often unnoted keeping the energies of the approximated and original filters equal results and two illustrative examples are presented

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

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

jordan triple multiplicative surjective maps on b h abstract let h be a hilbert space and b h be the algebra of all bounded linear operators on h in this paper we obtain a structure theorem of maps preserving the jordan triple zero product on b h then this is applied to give a full characterization of a surjective map b h b h satisfying a b a a b a

upper bounds of error probabilities for stationary gaussian channels with feedback in this paper we discuss the coding schemes and error probabilities in information transmission over additive gaussian noise channels with feedback where the gaussian noise processes are stationary but not necessarily white in the case of the white gaussian channel it is known that the minimum error probability under the average power constraint decreases faster than the exponential of any order recently gallager and nakiboglu 2010 proposed a coding scheme for the white gaussian channel and successfully showed the multiple exponential decay of the error probability for all rates below capacity this paper aims to prove that without any special assumptions on the noise of the stationary gaussian channel the minimum error probability decreases multiple exponentially fast in general no explicit formulas are known for the capacity of the stationary gaussian channel in this paper we introduce a lower bound c on the capacity c then we prove that the minimum error probability decreases multiple exponentially fast for all rates below c but not for all rates below c in the process of proving the scheme proposed by gallager and nakiboglu proves itself to be quite useful even though the gaussian channel is not white

additive mappings preserving operators of rank one abstract let b x be the algebra of all bounded linear operators on a nontrivial real or complex banach space and let f x be the subalgebra of all finite rank operators a characterization of additive mappings on f x which preserve operators of rank one or projections of rank one is given in the real case such mappings are automatically linear

some multiplicative preservers on b h abstract in this paper we describe the form of those continuous multiplicative maps on b h h being a separable complex hilbert space of dimension not less than 3 which preserve the rank or the corank furthermore we characterize those continuous presup semigroup endomorphisms of b h which are spectrum non increasing

jordan maps on triangular algebras abstract let t be a triangular algebra and r be an arbitrary ring suppose that m t r and m r t are surjective maps such that m am x m x a m a x xm a m m a x xm a am x m x a for all a t x r in this paper we give sufficient conditions on t such that both m and m are additive in particular if t is a standard subalgebra of a nest algebra then both m and m are additive

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

additivity of jordan elementary maps on nest algebras abstract let a be a standard subalgebra of a nest algebra on a hilbert space of dimension greater than one and b an arbitrary algebra a jordan elementary map of a b is a pair m m where m a b and m b a are two maps satisfying m am b a m a bm a m bm a b m b am b for a a b b in this note it is proved that for a special class of surjective jordan elementary maps of a b every member in it is automatically additive also we construct a counterexample which shows that this result is not necessarily true for all surjective jordan elementary maps