limits of hypercyclic and supercyclic operators abstract an operator t on a complex separable infinite dimensional hilbert space h is hypercyclic if there is a vector y in h such that the orbit y ty t2y is dense in h it is shown that if t is hypercyclic then t does not have any eigenvalue and that the union of the spectrum of t and the unit circle is a connected set this result is used to obtain a spectral characterization of the norm closure of the class hc h of all hypercyclic operators acting on h as well as a formula for the distance from a given operator to hc h analogous results are obtained for the closely related class sc h of all supercyclic operators this paper includes some information about the structure of the set of all hypercyclic supercyclic vectors of a given hypercyclic supercyclic resp operator t

supercyclic subspaces spectral theory and weighted shifts abstract a vector x in a banach space b is called hypercyclic for a bounded operator t if the orbit t n x n 0 is dense in b if the scalar multiples of the elements in the orbit are dense then the vector x is called supercyclic we give a general sufficient condition for a bounded operator on a banach space to have an infinite dimensional closed subspace of supercyclic vectors as a consequence we also obtain a spectral sufficient condition for the existence of such a subspace for an operator these results allow us to characterize unilateral and bilateral weighted shifts that have an infinite dimensional closed subspace of supercyclic vectors surprisingly there are weighted shift operators that have supercyclic vectors but in which all closed subspaces of supercyclic vectors are finite dimensional our results complement recent work on hypercyclic subspaces and supercyclic subspaces they also suggest that the problem of the existence of infinite dimensional closed subspaces of supercyclic vectors is not only different but also more difficult to handle than the corresponding problem for hypercyclic vectors

on multiple objective optimization with generalized univexity abstract a multiple objective optimization problem involving generalized univex functions is considered kuhn tucker type sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution mond weir type duality results are obtained further a vector valued lagrangian is introduced and certain vector saddlepoint results are presented

constant norm scrambled sets for hypercyclic operators abstract let t x x be a hypercyclic operator of a banach space x let d t x x x has a dense t orbit and let x r x x x r for r 0 we show that there is a linearly independent subset s d t with the following properties i for any r 0 and any nonempty relatively open subset u of x r the intersection s u is uncountable ii s s d t 0 and in particular l i m i n f n t n a t n b 0 and l i m s u p n t n a t n b for any two distinct a b s

dynamics of phase separation of a simple fluid mixture comparison between molecular dynamics and numerical integration of the phenomenological equation the dynamics of phase separation of fluid mixture is discussed numerical simulations in two dimensions are done both by means of the molecular dynamics at constant temperature and by the numerical integration of a phenomenological kinetic equation using a simplified interparticle potential we find that final results in the molecular dynamics are seriously affected by numerical errors the growth exponent of phase separating domains varies from 1 3 to 2 3 due to the numerical errors for a low viscosity fluid mixture with a critical composition the exponent 2 3 is observed in the case where the numerical error is ineffective on the other hand the numerical error in the numerical integration of the phenomenological equation is not serious and we obtain the growth exponent 2 3 as has been observed by many other similar numerical analyses we also discuss possibilities of new growth exponents that are simultaneously associated with the inertia and the dissipation

weyl s theorem and hypercyclic supercyclic operators abstract necessary and sufficient conditions for hypercyclic supercyclic banach space operators t to satisfy a t w a t 00 a t are proved

mean ergodic composition operators on banach spaces of holomorphic functions abstract given a symbol i e a holomorphic endomorphism of the unit disc we consider the composition operator c f f defined on the banach spaces of holomorphic functions a d and h d we obtain different conditions on the symbol which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces these conditions are related to the asymptotic behavior of the iterates of the symbol finally we deal with some particular case in the setting of weighted banach spaces of holomorphic functions

hypercyclic operators failing the hypercyclicity criterion on classical banach spaces abstract by a recent result of m de la rosa and c read there exist hypercyclic banach space operators which do not satisfy the hypercyclicity criterion in the present paper we prove that such operators can be constructed on a large class of banach spaces including c 0 n or l p n

simultaneous chaotic extensions for general operators on a hilbert subspace abstract for an infinite codimensional closed subspace m of a separable hilbert space h we show that every bounded linear operator a m h has a chaotic extension t h h as a generalization of this result we further show that for any uniformly bounded sequence of linear operators a n m h there exists a bounded linear operator v m h on the orthogonal complement m of m that simultaneously extends all operators a n to chaotic operators a n v h h

on universal subsets of banach spaces we prove that to most of the known hypercyclic operators a on separable banach spaces there exist compact compact convex compact connected subsets k of e such that each compact compact convex compact connected subset of e can be approximated with respect to hausdorff s distance by a n k for suitable n in mathbb n

property ω1 and weyl type theorem abstract in this note we define the property 1 a variant of weyl s theorem and establish for a bounded linear operator defined on a banach space the sufficient and necessary conditions for which property 1 holds by means of the variant of the essential approximate point spectrum 1 in addition the relation between property 1 and hypercyclicity or supercyclicity is discussed

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

lineability criteria with applications lineability is a property enjoyed by some subsets within a vector space x a subset a of x is called lineable whenever a contains except for zero an infinite dimensional vector subspace if additionally x is endowed with richer structures then the more stringent notions of dense lineability maximal dense lineability and spaceability arise naturally in this paper several lineability criteria are provided and applied to specific topological vector spaces mainly function spaces sometimes such criteria furnish unified proofs of a number of scattered results in the related literature families of strict order integrable functions hypercyclic vectors non extendable holomorphic mappings riemann non lebesgue integrable functions sequences not satisfying the lebesgue dominated convergence theorem nowhere analytic functions bounded variation functions entire functions with fast growth and peano curves among others are analyzed from the point of view of lineability

morphology of spinodal decomposition the morphology of homogeneous phases during spinodal decomposition i e the scaling of the content shape and connectivity of spatial structures is described by a family of morphological measures known as minkowski functionals besides providing means to determine the characteristic length scale l in a statistically robust and computationally inexpensive way the measures allow also one to define the crossover from the early stage decomposition to the late stage domain growth we observe the scaling behavior l ensuremath sim t ensuremath alpha with ensuremath alpha 1 3 ensuremath alpha 1 2 and ensuremath alpha 2 3 depending on the viscosity when approaching the spinodal ensuremath rho mathrm sp we recover the prediction l ensuremath sim ensuremath rho ensuremath ensuremath rho mathrm sp ensuremath 1 2 for the early time decomposition

browder essential approximate point spectra and hypercyclicity for operator matrices abstract when a b h and b b k are given we denote by m c the operator acting on the infinite dimensional separable hilbert space h k of the form m c a c 0 b in this paper it is shown that if a is upper semi fredholm of finite ascent and infinite codimension and if r b is closed of infinite kernel then m c is upper semi fredholm of finite ascent for some c b k h in addition we explore the hypercyclicity and supercyclicity for 2 2 upper triangular operator matrices on the hilbert space

semi fredholm theory hypercyclic and supercyclic subspaces a vector x in a banach space cal b is called hypercyclic for a bounded linear operator t cal b rightarrow cal b if the orbit t n x n geq 1 is dense in cal b we prove that if t is hereditarily hypercyclic and its essential spectrum meets the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is also true even if t is not hereditarily hypercyclic in this way we improve and extend to banach spaces a recent result for hilbert spaces we also investigate the corresponding problem for supercyclic operators in this case we obtain a description of the norm closure of the class of all supercyclic operators that have an infinite dimensional closed subspace of hypercyclic vectors moreover for certain kinds of supercyclic operators we can characterize when they have an infinite dimensional closed subspace of supercyclic vectors 1991 mathematics subject classification 47b38 47b99

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

multiparticle random walks on a deformable medium multiparticle random walks on a deformable medium have been investigated in 2 1 dimensions the time evolution of the particle distribution is studied the results show that the randomly distributed particles in the beginning will be self organized into a cluster pattern in the intermediate stage and then return to the random distribution pattern in the late stage the dependence of the clustering degree on the stiffness parameter of medium ensuremath alpha stability parameter of systems ensuremath beta and average particle density ensuremath rho 0 is also investigated there exists an optimal clustering stability ensuremath beta p at which the system has the strongest clustering ability and corresponds to a maximum clustering coefficient ensuremath gamma p the dependence of the optimal clustering coefficient ensuremath gamma p on the stiffness ensuremath alpha and particle density ensuremath rho 0 is obtained and the landscape of the medium generated by particles is also investigated

higher order duality in multiobjective fractional programming with square root term under generalized higher order f α β p σ d v type i univex functions in this paper a new generalized class of higher order f d v type i univex function is introduced with some examples for a differentiable multiobjective programming mp then multiobjective fractional programming problem mfp is considered in which the numerator and denominator of objective functions contain square root of positive semidefinite quadratic form and the necessary and sufficient conditions for efficient solution for mfp are established under generalized higher order f d v type i univex functions again higher order dual program is proposed for mfp and the duality results are established under generalized of higher order f d v type i univex functions also some computational work has been done to substantiate the analysis

topologically transitive extensions of bounded operators let x be any banach space and t a bounded operator on x an extensionopen image in new window of the pair x t consists of a banach space open image in new window in which x embeds isometrically through an isometry i and a bounded operatoropen image in new window on open image in new window such that open image in new window when x is separable it is additionally required that open image in new window be separable we say that open image in new window is a topologically transitive extension of x t when open image in new window is topologically transitive on open image in new window i e for every pair open image in new window of non empty open subsets of open image in new window there exists an integer n such that open image in new window is non empty we show that any such pair x t admits a topologically transitive extension open image in new window and that when h is a hilbert space h t admits a topologically transitive extension open image in new window where open image in new window is also a hilbert space we show that these extensions are indeed chaotic

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

weakly supercyclic operators inspired by a recent result that a weakly hypercyclic operator may fail to be norm hypercyclic we show there exists a weakly supercyclic operator that fails to be norm supercyclic moreover despite a classical result of hilden and wallen that every unilateral weighted backward shift is supercyclic we show such an operator may have a weakly supercyclic vector that is not a norm supercyclic vector in addition to these results we extend a result of kitai by showing a hyponormal operator cannot be weakly hypercyclic

the role of the angle in supercyclic behavior abstract a bounded operator t acting on a hilbert space h is said to be supercyclic if there is a vector f h such that the projective orbit t n f n 0 and c is dense in h we use a new method based on a very simple geometric idea that allows us to decide whether an operator is supercyclic or not the method is applied to obtain the following result a composition operator acting on the hardy space whose inducing symbol is a parabolic linear fractional map of the disk onto a proper subdisk is not supercyclic this result finishes the characterization of the supercyclic behavior of composition operators induced by linear fractional maps and thus completes previous work of bourdon and shapiro

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

optimality and duality for multiple objective optimization under generalized type i univexity abstract in this paper we extend the classes of generalized type i vector valued functions introduced by aghezzaf and hachimi in j global optim 18 2000 91 101 to generalized univex type i vector valued functions and consider a multiple objective optimization problem involving generalized type i univex functions a number of kuhn tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution the mond weir and general mond weir type duality results are also presented

irregular vectors of hilbert space operators abstract a vector x in a hilbert space h is called irregular for an operator t h h provided that sup n t n x and inf n t n x 0 we establish some basic properties of operators having irregular vectors and present examples that highlight the relationship or lack thereof between irregularity and hypercyclicity

hypercyclic operators on non normable frechet spaces abstract every infinite dimensional separable non normable frechet space admits a continuous hypercyclic operator a large class of separable countable inductive limits of banach spaces with the same property is given but an example of a separable complete inductive limit of banach spaces which admits no hypercyclic operator is provided it is also proved that no compact operator on a locally convex space is hypercyclic

linear subsets of nonlinear sets in topological vector spaces for the last decade there has been a generalized trend in mathematics on the search for large algebraic structures linear spaces closed subspaces or infinitely generated algebras composed of mathematical objects enjoying certain special properties this trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis operator theory summability theory polynomials in banach spaces hypercyclicity and chaos and general functional analysis this expository paper is devoted to providing an account on the advances and on the state of the art of this trend nowadays known as lineability and spaceability

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

weyl type theorem and hypercyclic operators using a variant of the essential approximate point spectrum we give the necessary and sufficient conditions for t for which the a browder s theorem or the a weyl s theorem holds also the relation between hypercyclic operators or supercyclic operators and the operators which satisfy weyl type theorem is discussed

mixed type duality in multiobjective programming problems two mixed type duals are introduced for multiobjective programming and for multiobjective fractional programming respectively results about weak duality strong duality and strictly reverse duality are presented under more suitable conditions

sums of hypercyclic operators abstract every bounded operator on a complex infinite dimensional separable hilbert space can be written as the sum of two hypercyclic operators and also as the sum of two chaotic operators

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

another note on weyl s theorem weyl s theorem holds for an operator t on a banach space x when the complement in the spectrum of the weyl spectrum coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity this is close to but not quite the same as equality between the weyl spectrum and the browder spectrum which in turn ought to but does not guarantee the spectral mapping theorem for the weyl spectrum of polynomials in t in this note we try to explore these distinctions recall 2 4 6 that a bounded linear operator t e bl x x on a banach space x is fredholm if t x is closed and both t 1 0 and x cl tx are finite dimensional in this case we define the index of t by index t dim t 1 0 dim x t x an operator t e bl x x is called weyl if it is fredholm of index zero and is called browder if it is fredholm of finite ascent and descent equivalently 6 theorem 7 9 3 if t is fredholm and t ai is invertible for sufficiently small a 0 in c the fredholm essential spectrum uess t the weyl spectrum wess t and the browder spectrum wcmm t of t are defined by 0 1 jess t a e c t ai is not fredholm 0 2 wess t a e c t ai is not weyl and 0 3 wecssmm t e c tai is not browder evidently 0 4 jess t c wess t c wcomm t cess t u acc v t where we write acc k for the accumulation points of k c c and av t for the usual spectrum of t if we write iso k k acc k and 0 5 leftr t a e iso 5 t 0 dim tai 1 0 xo for the isolated eigenvalues of finite multiplicity and 6 9 8 3 4 0 6 troo t a5 t wcomm t for the riesz points of t then 6 theorem 9 8 4 with the help of the punctured neighbourhood theorem 0 7 iso v t jess t iso 5 t wess t troo t c 4left t received by the editors december 18 1995 1991 mathematics subject classification primary 47a10

mixed type duality for nondifferentiable multiobjective fractional programming under generalized d ρ φ θ type 1 univex function in this paper we introduced a new generalized class of d r h q type 1 univex function with an example we introduced the mixed duality problem mfxd of the nondifferentiable multiobjective fractional programming problem mfp where the objective and constraint functions involved are directionally differentiable also we established the duality results under generalized class of d r h q type 1 univex function

d ρ η θ invexity in multiobjective optimization abstract in this paper a generalization of convexity is considered in the case of multiobjective optimization problems where the functions involved are non differentiable under d invexity assumptions on the functions involved weak strong and converse duality results are proved to relate weak pareto efficient solutions of the multiobjective programming problems pvp dvp and mwd we have also established the karush kuhn tucker sufficient optimality condition

on mixed duality in mathematical programming abstract an incomplete lagrange function is introduced for a class of nonlinear programming problems which explains the reason behind the construction of the mond weir type dual a mixed type dual is presented for a class of fractional and generalized fractional programming problems and various duality theorems are established several duals already reported in the literature follow as special cases of this study

a nonlinear age and maturity structured model of population dynamics i basic theory a nonlinear model of age and maturity structured population dynamics is analyzed the population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth the existence and asymptotic behavior of solutions are studied

nondifferentiable multiobjective programming under generalized d univexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex strong pseudoinvex weak quasi invex weak pseudoinvex and strong quasi invex functions in aghezzaf and hachimi numer funct anal optim 22 2001 775 d invex functions in antczak europ j oper res 137 2002 28 and univex functions in bector et al univex functions and univex nonlinear programming proc admin sci assoc canada 1992 p 115 by utilizing the new concepts we derive a karush kuhn tucker sufficient optimality condition and establish mond weir type and general mond weir type duality results for the nondifferentiable multiobjective programming problem

linear structure of hypercyclic vectors abstract a vector x in a banach space b is called hypercyclic for a bounded linear operator t b b if the orbit t n x n 1 is dense in b our main result states that if t is a compact perturbation of an operator of norm 1 and satisfies an appropiate extra hypothesis then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t in particular the result applies to compact perturbations of the identity we also include applications to some weighted backward shifts and compact perturbations of the identity by weighted backward shifts this last result in combination with a recent one that states that every banach space admits an operator with a hypercyclic vector proves that in all banach space there is an operator t with an infinite dimensional closed subspace consisting except for zero of hypercyclic vectors the main result also applies to the differentiation operator and the translation operator t f z f z 1 on certain hilbert spaces consisting of entire functions

bihypercyclic bilinear mappings abstract we propose a notion of orbit for bilinear mappings on banach spaces this then leads us to the concept of bihypercyclic bilinear mappings that is of bilinear mappings with a dense orbit we provide some examples of such mappings and we obtain some basic properties of bihypercyclicity in our main result we show that every separable real or complex banach space supports a bihypercyclic bilinear mapping we also formulate some open problems

optimal growth of entire functions frequently hypercyclic for the differentiation operator we solve a problem posed by bonilla and grosse erdmann 2007 7 by constructing an entire function f which is frequently hypercyclic with respect to the differentiation operator and satisfies mf r cerr 1 4 where c 0 may be chosen arbitrarily small this growth rate is sharp we also obtain optimal results for minimal growth in terms of average lp norms among other tools the proof uses the rudin shapiro polynomials and heat kernel estimates

multiobjective programming under d invexity abstract in this paper a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable by considering the concept of pareto optimal solution and substituting d invexity for convexity the fritz john type and karush kuhn tucker type necessary optimality conditions and duality in the sense of mond weir and wolfe for nondifferentiable multiobjective programming are given

hypercyclic subspaces for frechet space operators abstract a continuous linear operator t x x is hypercyclic if there is an x x such that the orbit t n x is dense and such a vector x is said to be hypercyclic for t recent progress show that it is possible to characterize banach space operators that have a hypercyclic subspace i e an infinite dimensional closed subspace h x of except for zero hypercyclic vectors the following is known to hold a banach space operator t has a hypercyclic subspace if there is a sequence n i and an infinite dimensional closed subspace e x such that t is hereditarily hypercyclic for n i and t n i 0 pointwise on e in this note we extend this result to the setting of frechet spaces that admit a continuous norm and study some applications for important function spaces as an application we also prove that any infinite dimensional separable frechet space with a continuous norm admits an operator with a hypercyclic subspace

on the convex hull generated by orbit of operators let x be an infinite dimensional banach space and t be a bounded operator on x the operator t is said to be convex cyclic if the convex hull generated by orb t x is dense in x for some x x we characterize completely such operators on finite dimensional vector spaces some examples of pure convex cyclic operators on infinite dimensional banach spaces are provided and many hypercyclic like properties of such operators are considered

approximation by chaotic operators and by conjugate classes we show that every bounded linear operator on a separable infinite dimensional hilbert space h is the sum of two operators in the norm closure of the set of operators on h that are chaotic in the sense of devaney we also observe that the density of several classes of cyclic operators with respect to the strong operator topology may be derived from a result by hadwin et al proc amer math soc 76 1979 250 252

hypercyclic subspaces in omega abstract we show that any countable family of operators of the form p b where p is a non constant polynomial and b is the backward shift operator on the countably infinite product of lines has a common hypercyclic subspace

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

common supercyclic vectors for a path of operators abstract we examine common supercyclic vectors for a path of operators in particular we show that the path consisting of convex combinations of two arbitrary unilateral weighted backward shifts has a dense g set of common supercyclic vectors moreover we show there exists a path with a dense g set of common supercyclic vectors between a unilateral weighted backward shift which satisfies the supercyclicity criterion and an operator which does not lastly we provide an example of a path of unilateral weighted backward shifts that fails to have a common supercyclic vector

strong ergodic properties of a first order partial differential equation on etudie l equation differentielle d ordre 1 u t c x u x f x u pour t x 0 0 1 avec la condition initiale u 0 x v x pour x 0 1 on demontre l existence d une mesure invariante exacte ayant certaines proprietes supplementaires

spectral theory and hypercyclic subspaces a vector x in a hilbert space h is called hypercyclic for a bounded operator t h h if the orbit tnx n 1 is dense in h our main result states that if t satisfies the hypercyclicity criterion and the essential spectrum intersects the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is true even if t is a hypercyclic operator which does not satisfy the hypercyclicity criterion as a consequence other characterizations are obtained for an operator t to have an infinite dimensional closed subspace of hypercyclic vectors these results apply to most of the hypercyclic operators that have appeared in the literature in particular they apply to bilateral and backward weighted shifts perturbations of the identity by backward weighted shifts multiplication operators and composition operators the main result also applies to the differentiation operator and the translation operator t f z f z 1 defined on certain hilbert spaces consisting of entire functions we also obtain a spectral characterization of the norm closure of the class of hypercyclic operators which have an infinite dimensional closed subspace of hypercyclic vectors

structure and growth of the cluster in gas liquid transition of two dimensional fluid abstract molecular dynamics simulations have been performed for a two dimensional fluid with truncated morse potential quenched into the two phase region the cluster size and shape were used to study the domain growth and structure the power law growth of the characteristic length scale which was calculated through the mean cluster size i e l ta with a 1 2 and 1 3 was observed in the late stage the fractal dimension was obtained from the scaling relationship of the gyration radius of the clusters with the cluster numbers the structure factors showed scaling relationship when scaled with the characteristic length it is also found that the domain structures are sensitive to temperature and the thermal noise influences the growth exponent for the dilute system

totally hereditarily normaloid operators and weyl s theorem for an elementary operator abstract a hilbert space operator t b h is hereditarily normaloid notation t hn if every part of t is normaloid an operator t hn is totally hereditarily normaloid notation t thn if every invertible part of t is normaloid we prove that thn operators with bishop s property also thn contractions with a compact defect operator such that t 1 0 t 1 0 and non zero isolated eigenvalues of t are normal are not supercyclic take a and b in thn and let d a b denote either of the elementary operators in b b h a b and a b where a b x a x b x and a b x a x x b we prove that if non zero isolated eigenvalues of a and b are normal and b 1 0 b 1 0 then d a b is an isoloid operator such that the quasi nilpotent part h 0 d a b of d a b equals d a b 1 0 for every complex number which is isolated in d a b if additionally d a b has the single valued extension property at all points not in the weyl spectrum of d a b then d a b and the conjugate operator d a b satisfy weyl s theorem

operator on the space of rapidly decreasing functions with all non zero vectors hypercyclic abstract we construct a continuous linear operator t on the schwartz space s r d of rapidly decreasing functions such that each non zero orbit of t is dense the construction is inspired by the work of c read on similar operators on the space l 1 the construction due to the structure of a frechet space can be made significantly simpler than the original construction of read

generalized kato type operators and property ω under perturbations abstract in this note we give the definition of generalized kato type and establish for a bounded linear operator defined on a hilbert space the sufficient and necessary conditions for which property holds by means of the induced spectrum of generalized kato property in addition the stability of property is discussed

on a universality property of certain integral operators in this paper we establish a universality property of fourier and hankel convolution operators and dunkl transforms

d invexity and optimality conditions abstract in this paper a generalization of convexity called d invexity is introduced substituting d invex for convex we get some optimality conditions for nondifferentiable multiobjective programming the application is demonstrated by an example

notes on subspace hypercyclic operators a bounded linear operator t on a banach space x is called subspace hypercyclic for a subspace m if orb t x m is dense in m for a vector x m in this case we show that p t has a relatively dense range for every real or complex polynomial p which in turn answers a question posed in madore and martinez avendano 2011 8 as a consequence the algebraic structure of the set of subspace hypercyclic vectors can be described