environment induced superselection rules in markovian regime a generalization of the jacobs deleeuw glicksberg splitting for a quantum dynamical semigroup is introduced this generalization called the isometric sweeping decomposition is used to derive effective superselection rules in the quantum system

pointwise i convergence and i convergence in measure of sequences of functions let i p n be an ideal we say that a sequence yn n n of real numbers is i convergent to y r if for every neighborhood u of y the set of n s satisfying yn u is in i basing upon this notion we define pointwise i convergence and i convergence in measure of sequences of measurable functions defined on a measure space with finite measure we discuss the relationship between these two convergences in particular we show that for a wide class of ideals including erd s ulam ideals and summable ideals the pointwise i convergence implies the i convergence in measure we also present examples of very regular ideals such that this implication does not hold

nonlinear integral equations for finite volume excited state energies of the o 3 and o 4 nonlinear σ models we propose nonlinear integral equations for the finite volume one particle energies in the o 3 and o 4 nonlinear models the equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state tba equations proposed earlier results of numerical calculations based on the nonlinear integral equations and the excited state tba equations agree within numerical precision

some results related with statistical convergence and berezin symbols abstract the concept of discrete statistical abel convergence is introduced in terms of berezin symbols we present necessary and sufficient condition under which a series n 0 a n with bounded sequence a n n 0 of complex numbers is discrete statistically abel convergent by using concept of statistical convergence we also give slight strengthening of a result of gokhberg and krein on compact operators

extensions of the preiss differentiability theorem abstract the preiss differentiability theorem for lipschitz functions on banach spaces is generalized to locally lower upper semi lipschitz functions and several extensions are presented

uniform approximation of convex function in smooth banach spaces abstract this article is devoted to smooth approximation of convex functions on banach spaces with smooth norm we prove that if x is a smooth space and f is a w lower semicontinuous lipschitzian convex function on x then there exist two w lower semicontinuous g teaux differentiable convex function sequences f n n 1 and g n n 1 such that 1 f n f n 1 f and f g n 1 g n 2 f n f and g n f uniformly on x 3 cl x x d f n x x cl x x d g n x x x

differentiability and ball covering property in banach spaces abstract in this paper author proves that if x 1 and x 2 are g teaux differentiable space then x 1 and x 2 have the ball covering property if and only if x 1 x 2 p and x 1 x 2 have the ball covering property where x y p x 1 p y 2 p 1 p p 1 and x y max x y

dirichlet forms and markovian semigroups on standard forms of von neumann algebras we characterize w continuous markovian semigroups on a von neumann algebra m which are 0 symmetric w r t a faithful normal state 0in m in terms of quadratic forms on the hilbert space h of a standard form m h p j we characterize also symmetric strongly continuous contraction semigroups on a real hilbert space h which leave invariant a closed convex set in h in terms of a contraction property of the associated quadratic forms we apply the results to give criteria of essential selfadjointness for quadratic form sums and to give a characterization of w continuous markovian semigroups on m which commute with the modular automorphism group 0t

on statistical measure theory abstract the purpose of this paper is to unify various kinds of statistical convergence by statistical measure convergence and to present jordan decomposition of finitely additive measures it is done through dealing with the most generalized statistical convergence ideal convergence by applying geometric functional analysis and banach space theory we first show that for each type of ideal i 2 n convergence there exists a set s of statistical measures such that the measure s convergence is equivalent to the statistical convergence to search for jordan decomposition of measures of statistical type we show that the subspace x i span a a i is an ideal of the space l in the sense of banach lattice hence the quotient space l x i is isometric to a c k space we then prove that a statistical measure has a jordan decomposition if and only if its corresponding functional is norm attaining on l and which in turn induces an approximate null ideal preserved jordan decomposition theorem of finitely additive measures finally we show this characterization and the approximate decomposition theorem are true for finitely additive measures defined on a general measurable space

weak statistical convergence and weak filter convergence for unbounded sequences abstract for every weakly statistically convergent sequence x n with increasing norms in a hilbert space we prove that sup n x n n this estimate is sharp we study analogous problem for some other types of weak filter convergence in particular for the erdos ulam filters analytical p filters and f filters we present also a refinement of the recent aron garcia maestre result on weakly dense sequences that tend to infinity in norm

a smooth variational principle with applications to subdifferentiability and to differentiability of convex functions we show that typically lower semicontinuous functions on a banach space densely inherit lower subderivatives of the same degree of smoothness as the norm in particular every continuous convex function on a space with a g teaux weak hadamard frechet smooth renorm is densely g teaux weak hadamard frechet differentiable our technique relies on a more powerful analogue of ekeland s variational principle in which the function is perturbed by a quadratic like function this smooth variational principle has very broad applicability in problems of nonsmooth analysis

classical properties of infinite quantum open systems long time asymptotic properties of a class of environmentally induced dynamical semigroups on arbitrary von neumann algebras are discussed such a semigroup selects observables called effective observables which are immune to the process of decoherence and so evolve in a reversible automorphic way in particular it is shown that effective observables of the quantum system in the thermodynamic limit subjected to a specific interaction with another quantum system obey classical dynamics

nonlinear integral equations for complex affine toda models associated with simply laced lie algebras a set of coupled nonlinear integral equations nlie is derived for a class of models connected to the quantum group simply laced lie algebra which are solvable using the bethe ansatz these equations describe arbitrary excited states of a system with finite spatial length l they generalize the simpler nlie of the sine gordon massive thirring model to affine toda field theory with imaginary coupling constant as an application the central charge and all the conformal weights of the uv conformal field theory are extracted in a straightforward manner the quantum group truncation for q at a root of unity is discussed in detail in the uv limit we recover through this procedure the rcfts with extended conformal symmetry

two characterizations of super reflexive banach spaces by the behaviour of differences of convex functions abstract a function defined on a banach space x is called convex if it can be represented as a difference of two continuous convex functions in this work we study the relationship between some geometrical properties of a banach space x and the behaviour of the class of all convex functions defined on it more precisely we provide two new characterizations of super reflexivity in terms convex functions

finite size corrections for nested bethe ansatz models and conformal invariance the method presented permits us to systematically compute physical magnitudes for large but finite size in theories solvable by the nested bethe ansatz the value of the central charge c and the surface tension are explicitly calculable in this way for the fundamental vertex and spin models associated to simply laced lie algebras c turns out to be equal to the rank of the algebra

generic frechet differentiability of convex functions dominated by a lower semicontinuous convex function abstract in this paper an extended real valued proper lower semicontinuous convex function f on a banach space is said to have the frechet differentiability property fdp if every proper lower semicontinuous convex function g with g f is frechet differentiable on a dense g subset of int dom g the interior of the effective domain of g we show that f has the fdp if and only if the w closed convex hull of the image of the subdifferential map of f has the radon nikod m property this is a generalization of the main theorem in a paper by lixin and shuzhong to appear according to this result it also gives several new criteria of asplund spaces

long range deformations for integrable spin chains we present a recursion relation for the explicit construction of integrable spin chain hamiltonians with long range interactions based on arbitrary shortrange e g nearest neighbor integrable spin chains it allows us to construct an infinite set of conserved long range charges we explain the moduli space of deformation parameters by different classes of generating operators the rapidity map and dressing phase in the long range bethe equations are a result of these deformations the closed chain asymptotic bethe equations for long range spin chains transforming under a generic symmetry algebra are derived notably our construction applies to generalizations of standard nearest neighbor chains such as alternating spin chains we also discuss relevant properties for its application to planar d 4 n 4 and d 3 n 6 supersymmetric gauge theories finally we present a map between long range and inhomogeneous spin chains delivering more insight into the structures of these models as well as their limitations at wrapping order

analytic characterizations of mazurʼs intersection property via convex functions abstract in this paper we present analytical characterizations of mazur s intersection property mip the cip and the mip via a specific class of convex functions and their conjugates more precisely let x be a banach space and x be its dual then x has the mip if and only if for every extended real valued lower semi continuous convex function f defined on x with bounded domain f is the supremum of all functions g f of the form g x r 0 r 2 x x 0 2 if x x 0 r otherwise for some x 0 x x and r 0 r r 0 and x has the cip if and only if for every extended real valued lower semi continuous convex function on x with relatively compact domain f is the infimum of all functions h f which are of the form h x r 0 1 x 2 x x 0 r 0 for all x x

light cone lattices and the exact solution of chiral fermion and sigma models a rich set of integrable two dimensional quantum field theories are obtained from integrable lattice vertex models with q states per bound q or 2 in the scaling limit by a generalisation of the light cone lattice approach chiral fermion models with any simple lie group of symmetry arise in this way for finite q as well as bosonic models like the principal chiral model for q infinity the hamiltonian momentum and colour conserved currents are constructed on the lattice and the bare equations of motion are derived the renormalised mass spectrum is given explicitly for the set of models considered here all these integrable vertex models yield conformal invariant theories if one takes the scalding limit in an appropriate different way it is argued that the values one obtains for the central charges are the same as those provided by the sugawara construction in the continuum for all simple lie algebras

mazur intersection property for asplund spaces abstract the main result of the present note states that it is consistent with the zfc axioms of set theory relying on martin s maximum mm axiom that every asplund space of density character 1 has a renorming with the mazur intersection property combined with the previous result of jimenez and moreno based upon the work of kunen under the continuum hypothesis we obtain that the mip renormability of asplund spaces of density 1 is undecidable in zfc

generalized mehler semigroups and applications we construct and study generalized mehler semigroups p t t 0 and their associated markov processesm the construction methods for p t t 0 are based on some new purely functional analytic results implying in particular that any strongly continuous semigroup on a hilbert spaceh can be extended to some larger hilbert spacee with the embeddingh e being hilbert schmidt the same analytic extension results are applied to construct strong solutions to stochastic differential equations of typedx t c dw t ax t dt with possibly unbounded linear operatorsa andc onh on a suitably chosen larger spacee for gaussian generalized mehler semigroups p t t 0 with corresponding markov processm the associated non symmetric dirichlet forms ed e are explicitly calculated and a necessary and sufficient condition for path regularity ofm in terms of e d e is proved then using dirichlet form methods it is shown thatm weakly solves the above stochastic differential equation if the state spacee is chosen appropriately finally we discuss the differences between these two methods yielding strong resp weak solutions

tba equations for excited states in the sine gordon model we propose thermodynamic bethe ansatz tba integral equations for multi particle soliton fermion states in the sine gordon massive thirring model this is based on t system and y system equations which follow from the bethe ansatz solution in the light cone lattice formulation of the model even and odd charge sectors are treated on an equal footing corresponding to periodic and twisted boundary conditions respectively the analytic properties of the y system functions are conjectured on the basis of the large volume solution of the system which we find explicitly a simple relation between the tba y functions and the counting function variable of the alternative non linear integral equation destri devega equation description of the model is given at the special value 2 6 of the sine gordon coupling exact expressions for energy and momentum eigenvalues of one particle states are found

continuity and generators of dynamical semigroups for infinite bose systems abstract for a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations ccr we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von neumann algebra associated with a representation of the ccr then the explicit form of the generators of the extended semigroups is calculated

dirichlet forms and symmetric markovian semigroups on ccr algebras with respect to quasi free states employing the construction method of dirichlet forms on standard forms of von neumann algebras developed in infinite dimensional analysis quantum probability and related topics 2000 vol 3 no 1 pp 1 14 ref 1 we construct dirichlet forms and associated symmetric markovian semigroups on ccr algebras with respect to quasi free states more precisely let a h0 be the ccr algebra over a complex separable pre hilbert space h0 and let be a quasi free state on a h0 for any normalized admissible function f and complete orthonormal system cons gn h0 we construct a dirichlet form and corresponding symmetric markovian semigroup on the natural standard form associated to the gns representation of a h0 it turns out that the form is independent of admissible function f and cons gn chosen by analyzing the spectrum of the generator dirichlet operator of the semigroup we show that the semigroup is ergodic and tends to the equilibrium exponentially fast

convex risk measures for portfolio optimization and concepts of flexibility due to their axiomatic foundation and their favorable computational properties convex risk measures are becoming a powerful tool in financial risk management in this paper we will review the fundamental structural concepts of convex risk measures within the framework of convex analysis then we will exploit it for deriving strong duality relations in a generic portfolio optimization context in particular the duality relationship can be used for designing new efficient approximation algorithms based on nesterov s smoothing techniques for non smooth convex optimization furthermore the presented concepts enable us to formalize the notion of flexibility as the marginal risk absorption capacity of a technology or available resources

generic frechet differentiability of convex functions on non asplund spaces abstract let f be a continuous convex function on a banach space e this paper shows that every proper convex function g on e with g f is generically frechet differentiable if and only if the image of the subdifferential map f of f has the radon nikod m property and in this case it is equivalent to showing that the image of f is separable on each separable subspace of e

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

differentiability of lipschitz functions on banach spaces abstract the main result of this note says that if the norm of a banach space e is differentiable frechet gateaux or in some intermediate sense away from the origin then every locally lipschitz function defined on an open subset g of e is differentiable in the same sense at every point of some subset of g dense in g as the main corollary we prove that every lipschitz function on an asplund space is frechet differentiable on a dense set moreover in all these results the mean value theorem for the points of differentiability which is equivalent to the possibility of computing the clarke subdifferential from the points of differentiability is shown to hold

a smooth variational principle with applications to hamilton jacobi equations in infinite dimensions abstract we prove that if x is a banach space which admits a smooth lipschitzian bump function then for every lower semicontinuous bounded below function there exists a lipschitzian smooth function g on x such that f g attains its strong minimum on x thus extending a result of borwein and preiss we then show how the above result can be used to obtain existence and uniqueness results of viscosity solutions of hamilton jacobi equations in infinite dimensional banach spaces a without assuming the radon nikodym property

ergodic properties of diffusion type quantum dynamical semigroups we develop a framework for investigation of asymptotic behavior of quantum markov semigroups on c algebras associated with noncommutative elliptic generators an exponential rate of convergence toward the projection onto the fixed point subalgebra has been established and in a particular case of the semigroup selecting rotationally invariant states of a three dimensional quantum system the time factor of such a convergence has been estimated

a characterization of banach spaces with separable duals via weak statistical convergence abstract let b be a banach space a b valued sequence xk is weakly statistically null provided lim n 1 n k n f x k e 0 for all e 0 and every continuous linear functional f on b a banach space is finite dimensional if and only if every weakly statistically null b valued sequence has a bounded subsequence if b is separable b is separable if and only if every bounded weakly statistically null b valued sequence contains a large weakly null sequence a characterization of spaces containing an isomorphic copy of l1 is given and it is also shown that l2 has a statistical m basis which is not a schauder basis

a measure theoretical subsequence characterization of statistical convergence the concept of statistical convergence of a sequence was first introduced by h fast statistical convergence was generalized by r c buck and studied by other authors using a regular nonnegative summability matrix a in place of c1 the main result in this paper is a theorem that gives meaning to the statement s s converges to l statistically t if and only if most of the subsequences of s converge in the ordinary sense to l here t is a regular nonnegative and triangular matrix corresponding results for lacunary statistical convergence recently defined and studied by j a fridy and c orhan are also presented introduction the concept of the statistical convergence of a sequence of reals s sn was first introduced by h fast 9 the sequence s sn is said to converge statistically to l and we write lim s l stat if for every e n oo rim n k e1 0 where jai denotes the cardinality of the set a properties of statistically convergent sequences were studied in 5 6 12 and 16 in 13 fridy and miller gave a characterization of statistical convergence for bounded sequences using a family of matrix summability methods statistical convergence can be generalized by using a regular nonnegative summability matrix a in place of c this idea was first mentioned by r c buck 3 in 1953 and has been further studied by sember and freedman 10 and 11 and connor 5 and 7 regular nonnegative summability matrices turn out to be too general for our purposes here instead we use the concept of a mean a matrix t amn will be called a mean if amn 0 when n m e iamn 1 for all m and limm 0oam 0 for each n if t amn is a mean following buck a sequence s sn is said to be statistically t summable to l and we write sn l stat t if for every e 0 received by the editors august 18 1993 and in revised form february 14 1994 originally communicated to the proceedings of the ams by andrew bruckner 1991 mathematics subject classification primary 40d25 secondary 40g99 28a12 1995 american mathematical society 0002 9947 95 1 00 s 25 per page

convex sets which are intersections of closed balls in this paper we aim to investigate different questions concerning the stability of the set m of all intersections of closed balls in a normed space we are mainly concerned with i the stability of m under the closure of the vector sums ii the stability under the addition of balls we prove that i and ii are different properties which have strong connections with the geometry of the space they have interest both in finite and infinite dimension in the former case there is a link with linear programming theory we also study two more stability properties related to the well known binary intersection property mazur sets and mazur spaces are introduced as a natural family satisfying i we prove that every two dimensional normed space is a mazur space a result which distinguishes dimension d 2 from dimension d 3 we also discuss the connections between mazur spaces and porosity

smooth approximation of convex functions in banach spaces abstract this paper shows that every extended real valued lower semi continuous proper respectively lipschitzian convex function defined on an asplund space can be represented as the point wise limit respectively uniform limit on every bounded set of a sequence of lipschitzian convex functions which are locally affine hence c at all points of a dense open subset and shows an analogous for w lower semi continuous proper respectively lipschitzian convex functions defined on dual spaces whose pre duals have the radon nikodym property

generalized statistical convergence and convergence free spaces abstract many results about statistical convergence in a general setting can be derived by consideration of the convergence free space of null sequences and its related cofilter and filter we derive algebraic and order properties preservation under uniform convergence cauchy properties and properties of cluster points we also show that for certain types of statistical convergence stronger convergence properties also hold finally we discuss the relationship between generalized statistical convergence and subsets of the stone cech compactification of the integers