differences of weighted composition operators from bloch space to h on the unit ball abstract in this paper we study the boundness and compactness of differences of weighted composition operators from the bloch space b to the space h of bounded analytic functions on the open unit ball of c n moreover we estimate the norm and the essential norm of differences of composition operators from b to h

fixed point composition and toeplitz composition c algebras abstract let be a linear fractional non automorphism self map of d that fixes t and satisfies 1 and consider the composition operator c acting on the hardy space h 2 d we determine which linear fractionally induced composition operators are contained in the unital c algebra generated by c and the ideal k of compact operators we apply these results to show that c c k and c f the unital c algebra generated by all composition operators induced by linear fractional non automorphism self maps of d that fix are each isomorphic modulo the ideal of compact operators to a unitization of a crossed product of c 0 0 1 we compute the k theory of c c k and calculate the essential spectra of a class of operators in this c algebra we also obtain a full description of the structures modulo the ideal of compact operators of the c algebras generated by the unilateral shift t z and a single linear fractionally induced composition operator

linear response for systems far off equilibrium abstract the kubo theory of linear response is extended with respect to reference states being excited far off equilibrium using the time dependent projector technique generalized response functions are introduced the structure of the corresponding evolution equations is mainly determined by the observable algebra of the relevant subspace generalizations of retarded green s functions may be introduced in the limit of two well separated time scales of evolution but generally the energy representation becomes unsuitable in systems far off equilibrium after a reformulation of the evolution superoperator a transparent example of a two level system is considered where the exciting laser pulse has the shape of a gaussian envelope

difference of weighted composition operators abstract we obtain complete characterizations in terms of carleson measures for bounded compact differences of weighted composition operators acting on the standard weighted bergman spaces over the unit disk unlike the known results we allow the weight functions to be non holomorphic and unbounded as a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the hardy spaces in terms of carleson measures and as a nontrivial application of this we show that compact differences of composition operators with univalent symbols on the hardy spaces are exactly the same as those on the weighted bergman spaces as another application we show that an earlier characterization due to acharyya and wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of non holomorphic weights we also include some explicit examples related to our results

critical behaviour of the non equilibrium ising model with locally competing temperatures the author uses a method which combines the ideas of the renormalisation group and mean field theory to obtain the phase diagram of two and three dimensional non equilibrium ising models with two locally competing temperatures comparison is made with available results of other authors an estimate of critical exponent nu is derived

essential norms of weighted composition operators and aleksandrov measures abstract we derive exact formulas for the essential and weak essential norms of weighted analytic composition operators acting on certain function spaces in the unit disc extending and improving earlier results due to sarason and to kriete and moorhouse differences of composition operators are also considered the formulas involve the aleksandrov measures associated to the symbol of the operator the results are based on a variant of a general method due to weis of constructing best compact and weakly compact approximants for linear operators on l 1 spaces

compact differences of composition operators abstract a characterization of compact difference is given for composition operators acting on the standard weighted bergman spaces and necessary conditions are given on a larger scale of weighted dirichlet spaces conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts the additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component

isotropic majority vote model on a square lattice the stationary critical properties of the isotropic majority vote model on a square lattice are calculated by monte carlo simulations and finite size analysis the critical exponents and are found to be the same as those of the ising model and the critical noise parameter is found to beqc 0 075 0 001

hilbert schmidt differences of composition operators on the bergman space in the setting of the weighted bergman space over the unit disk we characterize hilbert schmidt differences of two composition operators in terms of integrability condition involving pseudohyperbolic distance between the inducing functions we also show that a linear combination of two composition operators can be hilbert schmidt except for trivial cases only when it is essentially a difference we apply our results to study the topological structure of the space of all composition operators under the hilbert schmidt norm topology we first characterize components and then provide some sufficient conditions for isolation or for non isolation

necessary condition for compactness of a difference of composition operators on the dirichlet space abstract let be a self map of the unit disk and let c denote the composition operator acting on the standard dirichlet space d a necessary condition for compactness of a difference of two bounded composition operators acting on d is given as an application a characterization of disk automorphisms and for which the commutator c c is compact is given

on compactness of the difference of composition operators abstract let and be analytic self maps of the unit disc and denote by c and c the induced composition operators the compactness and weak compactness of the difference t c c are studied on h p spaces of the unit disc and l p spaces of the unit circle it is shown that the compactness of t on h p is independent of p 1 the compactness of t on l 1 and m the space of complex measures is characterized and examples of and are constructed such that t is compact on h 1 but non compact on l 1 other given results deal with l weakly compact counterparts of the previous results and a conjecture of j e shapiro

an application of atomic decomposition in bergman spaces to the study of differences of composition operators abstract in this paper we characterize bounded differences of composition operators from standard weighted bergman spaces a p into lebesgue spaces l q when 1 and p q in the process we also find an interesting connection between the difference operator and certain weighted composition operators answering a question raised in saukko 2011 18 by combining the results of this paper with those of saukko 2011 18 we obtain a complete characterization of bounded and compact differences between standard weighted bergman spaces

essential spectra of quasi parabolic composition operators on hardy spaces of analytic functions abstract in this work we study the essential spectra of composition operators on hardy spaces of analytic functions which might be termed as quasi parabolic this is the class of composition operators on h 2 with symbols whose conjugate with the cayley transform on the upper half plane are of the form z z z where h h and z 0 we especially examine the case where is discontinuous at infinity a new method is devised to show that this type of composition operator fall in a c algebra of toeplitz operators and fourier multipliers this method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra

spectral theory for algebraic combinations of toeplitz and composition operators abstract we determine the essential spectra of algebraic combinations of toeplitz operators with continuous symbol and composition operators induced by a class of linear fractional non automorphisms of the unit disk the operators in question act on the hardy space h 2 on the unit disk our method is to realize the c algebra that they generate as an extension of the compact operators by a concrete c algebra whose invertible elements are easily characterized

norms and essential norms of linear combinations of endomorphisms we compute norms and essential norms of linear combinations of endomorphisms on uniform algebras

difference of composition operators between different hardy spaces abstract some estimates for the norm and essential norm of the difference of two composition operators between different hardy spaces are given in this paper

compact linear combination of composition operators on bergman spaces abstract motivated by the question of shapiro and sundberg raised in 1990 study on linear combinations of composition operators has been a topic of growing interest in this paper we completely characterize the compactness of any finite linear combination of composition operators with general symbols on the weighted bergman spaces in two classical terms one is a function theoretic characterization of julia caratheodory type and the other is a measure theoretic characterization of carleson type our approach is completely different from what has been known so far

nonequilibrium spin models with ising universal behaviour the properties of a family of nonequilibrium spin models with up down symmetry on a square lattice are determined by a mean field pair approximation and by monte carlo simulation the phase diagram in the parameter space displays a critical line that terminates at a first order critical point it is found that the critical exponents are the same as those of the equilibrium ising model

majority vote model with different agents abstract we consider the majority vote model with noise in a network of social interactions for a system with two classes of individuals class and class for the two agent model each class has its own dynamics with individuals of class being influenced by neighbors of both classes while the individuals of type are influenced only by neighbors of that class we use monte carlo simulations and finite size scaling techniques to estimate the critical properties of the system in the stationary state the calculated values of the critical noise parameters q and q allow us to identify five distinct regions in the phase diagram on the q q plane the critical exponents for each class are the same and we conclude that the present model belongs to the same universality class as the two dimensional ising model

compact linear combinations of composition operators induced by linear fractional maps it has been known that the difference of two composition operators induced by linear fractional self maps of a ball cannot be nontrivially compact on either the hardy space or any standard weighted bergman space in this paper we extend this result in two significant directions the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension

linear relations in the calkin algebra for composition operators we consider this and related questions when is a finite linear combination of composition operators acting on the hardy space or the standard weighted bergman spaces on the unit disk a compact operator

entropy production in the majority vote model we analyzed the entropy production in the majority vote model by using a mean field approximation and monte carlo simulations the dynamical rules of the model do not obey detailed balance so that entropy is continuously being produced this nonequilibrium stochastic model is known to have a critical behavior belonging to the universality class of the equilibrium ising model we show that the entropy production exhibits a singularity at the critical point whose exponent is estimated numerically

weighted composition operators between hilbert spaces of analytic functions in the operator norm and hilbert schmidt norm topologies abstract we here investigate the topological structure of the space of weighted composition operators boundedly acting between two hilbert spaces of analytic functions on the open unit disk satisfying some natural hypotheses we will consider the operator norm topology and the hilbert schmidt norm topology respectively these results will be involved in the investigation for the explicit cases of the classical hardy hilbert space the weighted bergman spaces and the dirichlet space furthermore we will estimate the hilbert schmidt norms of difference of two composition operators acting from the dirichlet space to the hardy and the weighted bergman spaces

majority vote model with a bimodal distribution of noises in small world networks abstract we consider a generalized version of the majority vote model in small world networks in our model each site of the network has noise q 0 and q 0 with probability f and 1 f respectively the connections of the two dimensional square lattice are rewired with probability p we performed monte carlo simulations to characterize the order disorder phase transition of the system through finite size scaling analysis we calculated the critical noise value q c and the standard critical exponents 1 our results suggest that these exponents are different from those of the isotropic majority vote model we concluded that the zero noise fraction f when combined with the rewiring probability p drive the system to a different universality class from that of the isotropic majority vote model

anisotropic voter model a majority vote model subject to anisotropic voting rules is studied in two dimensions using a first order mean field approximation and monte carlo simulations the critical behavior is consistent with the 2d ising universality class

differences of generalized composition operators on the bloch space abstract the boundedness and compactness of the differences of two generalized composition operators on the bloch space in the unit disk are investigated in this paper

joint carleson measure and the difference of composition operators on aαp bn we introduce a concept of joint carleson measure and characterize when the difference of two composition operators on a p bn the weighted bergman space over the unit ball bn in cn is bounded or compact we apply this joint carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n 2 this is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p 0 moreover the compact difference on the weighted bergman spaces over the unit disc is known to be independent of p 0 and the compact difference on a p bn is known to be independent of p 0 if each composition operator is bounded on a p bn for some 1 2

difference of composition operators between standard weighted bergman spaces we obtain estimates for the norm and essential norm of the difference of two composition operators between certain bergman spaces in particular a necessary and sufficient condition for boundedness and compactness of the operator is established finally we give a sufficient condition for boundedness and compactness of the difference operator between hardy spaces

which linear fractional composition operators are essentially normal abstract we characterize the essentially normal composition operators induced on the hardy space h2 by linear fractional maps they are either compact normal or the nontrivial case induced by parabolic nonautomorphisms these parabolic maps induce the first known examples of nontrivially essentially normal composition operators in addition we characterize those linear fractionally induced composition operators on h2 that are essentially self adjoint and present a number of results for composition operators induced by maps that are not linear fractional

on the connected component of compact composition operators on the hardy space we show that there exist non compact composition operators in the connected component of the compact ones on the classical hardy space h2 this answers a question posed by shapiro and sundberg in 1990 we also establish an improved version of a theorem of maccluer giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols as a main tool we use aleksandrov clark measures

compact double differences of composition operators on the bergman spaces abstract as is well known on the weighted bergman spaces over the unit disk compactness of differences of two composition operators is characterized by certain cancellation property of the inducing maps at every bad boundary point which makes each composition operator in the difference fail to be compact recently the second and third authors obtained a result implying that double difference cancellation is not possible for linear combinations of three composition operators in this paper we obtain a complete characterization for compact double differences formed by four composition operators applying our characterization we easily recover known results on linear combinations of two or three composition operators as another application we also show that double difference cancellation is possible for linear combinations of four composition operators by constructing an explicit example of a compact double difference formed by two noncompact differences in spite of such an example our characterization also shows that double difference cancellation may occur in the global sense only and that genuine double difference cancellation is not possible in a certain local sense

topological structure of the set of composition operators on the weighted bergman space abstract we investigate the topological connectedness of the set of composition operators on the weighted bergman space a 2 under the uniform operator topology one of our main results is to first find a necessary and sufficient condition for two composition operators on a 2 to be linearly connected in the case of one variable as a corollary we show that two composition operators on a 2 with compact difference must lie in the same path component

non equilibrium ising model with competing glauber dynamics the authors consider a kinetic ising model with ferromagnetic interactions that evolves in time according to two competing glauber dynamics at different temperatures the steady states of this non equilibrium model are studied by using a dynamic pair approximation when the temperatures are low enough the system orders in a ferromagnetic state but if one of the temperatures is allowed to be negative the system may have an antiferromagnetic order they obtain the phase diagram for the case of a square lattice in this case they calculate the critical exponent v by using a mean field renormalization group method the numerical results indicate that the model falls into the same universality class of the equilibrium ising model they also show that one particular case of the non equilibrium model studied here is equivalent to the majority vote model

unique floquet decomposition theory near resonance in quantum systems abstract a response theory in quantum systems which can discuss the stability of the total system and the appearance of subharmonics is proposed the propagator of the system in the liouville space is decomposed into the periodic factor with the same frequency as the external field and the remaining factor by using the unique floquet decomposition theory the relation between the usual floquet operator and the remaining factor is studied it is shown that the remaining factor is responsible for the stability of the total system and the appearance of subharmonics a quantum version of mathieu s equation is studied as an application of the general theory the stability condition of subharmonics is shown to coincide with the classical one it is also shown that the drastic change of energy spectrum occurs if the subharmonic oscillation is unstable the energy spectrum is continuous while in the stable case the energy spectrum is discrete

cumulants of the three state potts model and of nonequilibrium models with c3v symmetry the critical behaviour of two dimensional stochastic lattice gas models with c3v symmetry is analysed we study the cumulants of the order parameter for the three state equilibrium potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group c3v by means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems in particular we find that the binder reduced fourth order cumulant takes a universal value u which is the same for the three state potts model and for the irreversible models the same universal behaviour is observed for the reduced third order cumulant

linear sums of two composition operators on the fock space abstract linear sums of two composition operators of the multi dimensional fock space are studied we show that such an operator is bounded only when both composition operators in the sum are bounded so cancelation phenomenon is not possible on the fock space in contrast to what have been known on other well known function spaces over the unit disk we also show the analogues for compactness and for membership in the schatten classes for linear sums of more than two composition operators the investigation is left open

essentially normal composition operators on h2 abstract we prove a simple criterion for essential normality of composition operators on the hardy space induced by maps in a reasonably large class s of analytic self maps of the unit disk by combining this criterion with boundary caratheodory fejer interpolation theory we exhibit a parametrization for all rational self maps of the unit disk which induce essentially normal composition operators

topological structures of the sets of composition operators on the bloch spaces we study properties of the topological sets of composition operators on bloch and little bloch spaces in the operator topology

steady state of periodically driven systems in quantum statistics abstract a formal theory for the statistical operator of the steady state in periodically driven matter is given for this purpose the periodic fields are changed to have an amplitude increasing with e t where is taken to be zero at the end this procedure allows for a correct description of energy denominators the results following from the steady state operator are compared with the long time behaviour obtained from n th order response and are shown to agree thus the proposed statistical operator has all properties required

differences of composition operators between weighted type spaces of holomorphic functions on the unit ball of cn we consider differences of composition operators between weighted type or little weighted type spaces of analytic functions on the unit ball with weighted sup norms and give estimates for the distance of these differences to the space of compact operators we also study the boundedness and compactness of these operators

cancellation properties of composition operators on bergman spaces abstract the compact difference of two composition operators on the bergman spaces over the unit disc is characterized in 11 in terms of certain cancellation property of the inducing maps at every bad boundary points which make each single composition operator not to be compact in this paper we completely characterize the compactness of a linear combination of three composition operators on the bergman space as one consequence of this characterization we show that there is no cancellation property for the compactness of double difference of composition operators more precisely we show that if i are distinct and none of c i is compact then c 1 c 2 c 3 c 1 is compact if and only if both c 1 c 2 and c 3 c 1 are compact

majority vote model with a bimodal distribution of noises abstract we consider the majority vote dynamics where the noise parameter associated with each spin on a two dimensional square lattice is a bimodally distributed random variable defined as q with probability 1 f or zero with probability f where 0 f 1 is the proportion of noiseless sites we use monte carlo simulations and finite size scaling theory to characterize the ordered and disordered phases and study the phase transition of the model we conclude that in the thermodynamic limit the value of the critical noise below which there exists an ordered phase increases with f the fraction of sites with zero noise the calculation of the critical exponents shows that the introduction of disorder in the noise parameter does not alter the ising critical behavior of the model system

components of linear fractional composition operators abstract we determine when two linear fractional composition operators on the hardy space h 2 belong to the same component in the collection of all composition operators on h 2 we show that two such composition operators in the same component may fail to have compact difference which answers a question raised by joel shapiro and carl sundberg