asymptotic type for sectorial operators and an integral of fractional powers abstract there is a standard notion of type for a sectorial linear operator acting in a banach space we introduce a notion of asymptotic type for a linear operator v involving estimates on the resolvent i v 1 as 0 we show for example that if v is sectorial and of asymptotic type then the fractional power v is of asymptotic type for a suitable range of positive moreover we establish various properties of the operator 0 1 d v in particular this operator is of asymptotic type 0 for a sectorial operator v this result has an application to the construction of operators satisfying the well known ritt resolvent condition

remarks on rates of convergence of powers of contractions abstract we prove that if the numerical range of a hilbert space contraction t is in a certain closed convex set of the unit disk which touches the unit circle only at 1 then t n i t o 1 n with 1 2 1 for normal contractions the condition is also necessary another sufficient condition for 1 2 necessary for t normal is that the numerical range of t be in a disk z z 1 for some 0 1 as a consequence of results of seifert we obtain that a power bounded t on a hilbert space satisfies t n i t o 1 n with 0 1 if and only if sup 1 2 1 1 r t when t is a contraction on l 2 satisfying the numerical range condition it is shown that t n f n 1 converges to 0 a e with a maximal inequality for every f l 2 an example shows that in general a positive contraction t on l 2 may have an f 0 with lim sup t n f log n n a e

functional calculus estimates for tadmor ritt operators abstract we show h functional calculus estimates for tadmor ritt operators also known as ritt operators which generalize and improve results by vitse these estimates are in conformity with the best known power bounds for tadmor ritt operators in terms of the constant dependence furthermore it is shown how discrete square function estimates influence the functional calculus estimates

subordinated discrete semigroups of operators given a power bounded linear operator t in a banach space and a probability f on the non negative integers one can form a subordinated operator s k 0 f k t k we obtain asymptotic properties of the subordinated discrete semigroup s n n 1 2 under certain conditions on f in particular we study probabilities f with the property that s satisfies the ritt resolvent condition whenever t is power bounded examples and counterexamples of this property are discussed the hypothesis of power boundedness of t can sometimes be replaced by the weaker kreiss resolvent condition

a besov class functional calculus for bounded holomorphic semigroups abstract it is well known that 2 sectorial operators generally do not admit a bounded h calculus over the right half plane in contrast to this we prove that the h calculus is bounded over any class of functions whose fourier spectrum is contained in some interval e with 0 e the constant bounding this calculus grows as log e e as e and this growth is sharp over all banach space operators of the class under consideration it follows from these estimates that 2 sectorial operators admit a bounded calculus over the besov algebra b 1 0 of the right half plane we also discuss the link between 2 sectorial operators and bounded tadmor ritt operators

growth orders and ergodicity for absolutely cesaro bounded operators abstract in this paper we extend the concept of absolutely cesaro boundedness to the fractional case we construct a weighted shift operator belonging to this class of operators and we prove that if t is an absolutely cesaro bounded operator of order with 0 1 then t n o n generalizing the result obtained for 1 moreover if 1 then t n o n we apply such results to get stability properties for the cesaro means of bounded operators

limit theorems for markov chains by the symmetrization method abstract let p be a markov operator with invariant probability m ergodic on l 2 s m and let w n n 0 be the markov chain with state space s and transition probability p on the space of trajectories p m with initial distribution m following wu and olla we define the symmetrized operator p s p p 2 and analyze the linear manifold h 1 i p s l 2 s m we obtain for real f h 1 an explicit forward backward martingale decomposition with a coboundary remainder for such f we also obtain some maximal inequalities for s n f k 0 n f w k related to the law of iterated logarithm we prove an almost sure central limit theorem for f h 1 when p is normal in l 2 s m or when p satisfies the sector condition we characterize the sector condition by the numerical range of p on the complex l 2 s m being in a sector with vertex at 1 we then show that if p has a real normal dilation which satisfies the sector condition then h 1 i p l 2 s m we use our approach to prove that p is l 2 uniformly ergodic if and only if it satisfies the discrete poincare s inequality

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

efficient algorithms for the two dimensional ising model with a surface field the bond propagation and site propagation algorithms are extended to the two dimensional 2d ising model with a surface field with these algorithms we can calculate the free energy internal energy specific heat magnetization correlation functions surface magnetization surface susceptibility and surface correlations the method can handle continuous and discrete bond and surface field disorder and is especially efficient in the case of bond or site dilution to test these algorithms we study the wetting transition of the 2d ising model which was solved exactly by abraham we can locate the transition point accurately with a relative error of 10 8 we carry out the calculation of the specific heat and surface susceptibility on lattices with sizes up to 200 2 times 200 the results show that a finite jump develops in the specific heat and surface susceptibility at the transition point as the lattice size increases for lattice size 320 2 times 320 the parallel correlation length exponent is 1 86 while abraham s exact result is 2 0 the perpendicular correlation length exponent for lattice size 160 2 times 160 is 1 05 whereas its exact value is 1 0

symmetrizable finite difference operators we introduce the notion of a symmetrizable finite difference oper ator and prove that such operators are stable we then present some sufficient conditions for symmetrizability one of these extends h o kreiss theorem on dissipative difference schemes for hyperbolic equations to a more general case with full jc invariable coefficients

dissipative operators on banach spaces a bounded linear operator t on a banach space is said to be dissipative if ett 1 for all t 0 we show that if t is a dissipative operator on a banach space then a limt ettt sup t ir b if t ir is contained in i 2 i 2 then limt ettsint sup sin t ir some related problems are also discussed

doubly power bounded operators on lp 2 p 1 abstract we show the existence of a doubly power bounded t on l p 1 p p 2 such that t is spectral of scalar type hence polynomially bounded t is not similar to a lamperti operator hence is not similar to an isometry none of the powers of t is similar to a lamperti operator none of the powers is similar to a positive operator and for some f l p the averages 1 n k 1 n t k f or the averages along the primes or the squares fail to be a e convergent

iterates of markov operators and their limits abstract it is well known that iterates of quasi compact operators converge towards a spectral projection whereas the explicit construction of the limiting operator is in general hard to obtain here we show a simple method to explicitly construct this projection operator provided that the fixed points of the operator and its adjoint are known which is often the case for operators used in approximation theory we use an approach related to riesz schauder and fredholm theory to analyze the iterates of operators on general banach spaces while our main result remains applicable without specific knowledge on the underlying framework applications for markov operators on the space of continuous functions c x are provided where x is a compact hausdorff space

on the spectrum of positive linear operators with a partition of unity property abstract we characterize the spectrum of positive linear operators between banach function spaces having finite rank and a partition of unity property our main result states that all the points in the spectrum are eigenvalues and 1 is the only eigenvalue on the unit circle finally we show that the iterates converge in the uniform operator topology to a projection operator that reproduces constant functions and we provide a simple criterion to obtain the limiting projection operator

shape dependent finite size effect of the critical two dimensional ising model on a triangular lattice using a bond propagation algorithm we study the finite size behavior of the critical two dimensional ising model on a finite triangular lattice with free boundaries in five shapes triangular rhomboid trapezoid hexagonal and rectangular the critical free energy internal energy and specific heat are calculated the accuracy of the free energy reaches 10 26 based on accurate data on several finite systems with linear size up to n 2000 we extract the bulk surface and corner parts of the free energy internal energy and specific heat accurately we confirm the conformal field theory prediction that the corner free energy is universal and find logarithmic corrections in higher order terms in the critical free energy for the rhomboid trapezoid and hexagonal systems which are absent for the triangular and rectangular systems the logarithmic edge corrections due to edges parallel or perpendicular to the bond directions in the internal energy are found to be identical while the logarithmic edge corrections due to corresponding edges in the specific heat are different the corner internal energy and corner specific heat for angles 3 2 and 2 3 are obtained as well as higher order corrections comparing with the corner internal energy and corner specific heat we previously found on a rectangle of the square lattice phys rev e 86 041149 2012 we conclude that the corner internal energy and corner specific heat for the rectangular shape are not universal

functional calculus under the tadmor ritt condition and free interpolation by polynomials of a given degree for banach space operators t satisfying the tadmor ritt condition zi t 1 c z 1 1 z 1 we prove that the best possible constant ct n bounding the polynomial calculus for t p t ct n p deg p n behaves in the worst case as logn as n this result is based on a new free carleson type interpolation theorem for polynomials of a given degree

mean bounded operators and mean ergodic theorems abstract in any reflexive banach lattice the resolvent resp the cesaro means of a mean bounded semi group of operators resp of positive operators is resp are strongly convergent the mean ergodic theorem fails for mean bounded operators which are not necessarily positive

the asymptotic lift of a completely positive map starting with a unit preserving normal completely positive map l m m acting on a von neumann algebra or more generally a dual operator system we show that there is a unique reversible system n n i e a complete order automorphism of a dual operator system n that captures all of the asymptotic behavior of l called the asymptotic lift of l this provides a noncommutative generalization of the frobenius theorems that describe the asymptotic behavior of the sequence of powers of a stochastic n n matrix in cases where m is a von neumann algebra the asymptotic lift is shown to be a w dynamical system n z and we identify n z as the tail flow of the minimal dilation of l we are also able to identify the poisson boundary of l as the fixed algebra n in general we show the action of the asymptotic lift is trivial iff l is slowly oscillating in the sense that limn ln 1 ln 0 m hence is often a nontrivial automorphism of n the asymptotic lift of a variety of examples is calculated

continuous time kreiss resolvent condition on infinite dimensional spaces given the infinitesimal generator a of a c 0 semigroup on the banach space x which satisfies the kreiss resolvent condition i e there exists an m 0 such that vert si a 1 vert leq frac m mathrm re s for all complex s with positive real part we show that for general banach spaces this condition does not give any information on the growth of the associated c 0 semigroup for hilbert spaces the situation is less dramatic in particular we show that the semigroup can grow at most like t furthermore we show that for every gamma in 0 1 there exists an infinitesimal generator satisfying the kreiss resolvent condition but whose semigroup grows at least like t gamma as a consequence we find that for mathbb r n with the standard euclidian norm the estimate vert exp at vert leq m 1 min n t cannot be replaced by a lower power of n or t

theorems of katznelson tzafriri type for contractions for t a contraction on a hilbert space and a function in the disc algebra we show that if 0 on spt then limn t tn 0 the same method gives a new proof of recent results of katznelson tzafriri several applications are given

stability analysis of finite difference pseudospectral and fourier galerkin approximations for time dependent problems we consider finite difference pseudospectral and fourier galerkin methods for the approximate solution of time dependent problems the paper provides a unified framework for the stability analysis of all three discrete methods in particular the problem of stability for highly accurate stencils is studied in some detail

some results of katznelson tzafriri type abstract for semigroups s r z and z k we show that if t is a representation of s by contractions on a hilbert space then inf t s t t f t sup f sp u t s where f l 1 s and sp u t s is the unitary spectrum of t with respect to s for t a representation of a suitable semigroup s by contractions on a banach space we give sharp conditions on sp u t s which guarantee that the equality above holds these conditions concern the thinness of sp u t s in the harmonic analysis sense these results are related to theorems of katznelson tzafriri type which give conditions guaranteeing that inf t s t t f t vanishes

theorems of katznelson tzafriri type for semigroups of operators let s be a locally compact abelian semigroup and t a bounded representation of s by linear bounded operators in a banach space x with spectrum sp t let spu t be the intersection of sp t with the set of unitary characters of s we prove that if s r or if t is norm continuous and if f is a function in l1 s which is of spectral synthesis with respect to spu t then inft s sf s t t s ds 0

a generalization of sectorial and quasi sectorial operators abstract in the paper we generalize the main results presented in bentkus and paulauskas 2004 2 by giving rates of approximation of some semigroups of operators of the order n 0 1 also two classes of operators generalizing sectorial and quasi sectorial operators are introduced and their properties are studied

bounding partial sums of fourier series in weighted l 2 norms with applications to matrix analysis for integrable functions f defined on the interval we denote the partial sums of the corresponding fourier series by sn f n 0 1 2 in this paper we deal with the problem of bounding supn sn where denotes an operator norm induced by a weighted l2 norm for functions f on for weight functions w belonging to a class introduced by helson and szego ann mat pura appl 51 1960 107 we present explicit upper bounds for supn sn in terms of w the authors were led to the problem of deriving explicit upper bounds for supn sn by the need for such bounds in an analysis related to the kreiss matrix theorem a famous result in the fields of linear algebra and numerical analysis accordingly the present paper highlights the relevance of bounds on supn sn to these fields

weak admissibility does not imply admissibility for analytic semigroups two conjectures on admissible control operators by george weiss are disproved in this paper one conjecture says that an operator b defined on an infinite dimensional hilbert space u is an admissible control operator if for every element u in u the vector bu defines an admissible control operator the other conjecture says that b is an admissible control operator if a certain resolvent estimate is satisfied the examples given in this paper show that even for analytic semigroups the conjectures do not hold in the last section we construct a semigroup example showing that the first estimate in the hille yosida theorem is not sufficient to conclude boundedness of the semigroup

an extension of the kreiss matrix theorem a new condition is shown to be equivalent to the other conditions of the kreiss matrix theorem for power bounded families of matrices this new condition is important for the application of the theory of pseudodifference operators to stability estimates for variable coefficient finite difference equations as an example of the usefulness of this new condition it is used to prove stability of the leapfrog scheme for hyperbolic equations with variable coefficients

the equivalence of l2 stability the resolvent condition and strict h stability abstract the kreiss matrix theorem asserts that a family of n n matrices is l 2 stable if and only if either a resolvent condition r or a hermitian norm condition h is satisfied we give a direct considerably shorter proof of the power boundedness of an n n matrix satisfying r sharpening former results by showing that power boundedness depends at most linearly on the dimension n we also show that l 2 stability is characterized by an h condition employing a general h numerical radius instead of the usual h norm thus generalizing a sufficient stability criterion due to lax and wendroff

accurate expansions of internal energy and specific heat of critical two dimensional ising model with free boundaries the bond propagation algorithm for the specific heat of the two dimensional ising model is developed and that for the internal energy is completed using these algorithms we study the critical internal energy and specific heat of the model on the square lattice and triangular lattice with free boundaries comparing with previous works phys rev e 86 041149 2012 phys rev e 87 022124 2013 we reach much higher accuracy 10 28 of the internal energy and specific heat compared to the accuracy 10 11 of the internal energy and 10 9 of the specific heat reached in the previous works this leads to much more accurate estimations of the edge and corner terms the exact values of all edge and corner terms are therefore conjectured the accurate forms of finite size scaling for the internal energy and specific heat are determined for the rectangle shaped square lattice with various aspect ratios and various shaped triangular lattice for the rectangle shaped square and triangular lattices and the triangle shaped triangular lattice there is no logarithmic correction terms of order higher than 1 s with s the area of the system for the triangular lattice in rhombus trapezoid and hexagonal shapes there exist logarithmic correction terms of order higher than 1 s for the internal energy and logarithmic correction terms of all orders for the specific heat

herstein s lie theory revisited an associative ring r becomes a jordan ring r under x 0 y xy yx and a lie ring r under x y xy yx in case r has an involution i e an antiautomorphism of period 1 or 2 then the set of symmetric elements s s e r 1 s s is a jordan subring of r and the set of skew elements k ker 1 k k is a lie subring of rp in the early 1950s herstein initiated a study of the jordan and lie ideals of r s and k in case that r was a simple associative ring either without or with an involution in the ensuring years his work has been generalized in various directions on the one hand to the setting of prime and semiprime rings and on the other hand to invariance conditions other than that given by ideals besides herstein himself we mention lanski as having been a major force in this program their influence is certainly felt in the present paper we have taken the liberty of using various arguments without making specific mention from their papers notably 6 and s other important contributions in this area have also been made by baxter chacron erickson montgomery osborn streb and others part of our motivation in writing this paper is to obtain the lie ideal theory for semiprime rings with involution by a somewhat different approach from the self contained elementary very clever methods embodied in the original style of herstein let us describe very briefly the spirit of our approach for r a ring with involution and 1 any ideal i e an ideal invariant under in k k is always a lie ideal of k which we shall call a standard lie ideal of k a

uniform monotonicity of norms and the strong zero two law abstract recently rainer wittmann proved a strong zero two law for positive contractions of lp spaces 1 p

growth order and stability of discrete semigroups abstract characterizations of the growth order and the stability for the orbit t n x of the powers t n of a bounded linear operator t in terms of cesaro and abel means of the orbit are obtained it is also seen that under the tauberian condition n t n 1 t n o 1 the strong resp uniform convergence of t n is equivalent to its strong resp uniform abel mean convergence

uniform abel kreiss boundedness and the extremal behaviour of the volterra operator let v denote the classical volterra operator in this work sharp estimates of the norm of i v n acting on l p 0 1 for 1 leq p leq infty are obtained as a consequence i v acting on l p 0 1 with 1 leq p leq infty is power bounded if and only if p 2 thus the volterra operator characterizes when l p 0 1 is a hilbert space by means of sharp estimates of the l 1 norm of the n th partial sums of the generating function of the laguerre polynomials on the unit circle it is also proved that i v is uniformly kreiss bounded on the spaces l p 0 1 for 1 leq p leq infty a bounded linear operator t on a banach space is said to be kreiss bounded if there is a constant c 0 such that vert t lambda 1 vert leq c lambda 1 1 for lambda 1 if the same upper estimate holds for each of the partial sums of the resolvent then t is said to be uniformly kreiss bounded this is for instance true for power bounded operators for finite dimensional banach spaces kreiss matrix theorem asserts that kreiss boundedness is equivalent to t being power bounded thus in the infinite dimensional setting even a much stronger property than kreiss boundedness still does not imply power boundedness it is also shown that for general operators uniform abel boundedness characterizes ces ro boundedness and as a consequence uniform kreiss boundedness is characterized in terms of a ces ro type boundedness of order 1

the modulus of a regular linear operator and the zero two law in lp spaces 1 p p 2 abstract using the linear modulus of a regular operator we extend the zero two law for positive contractions of l p spaces 1 p p 2 the proof uses the approximate point spectrum of positive contractions and a procedure obtained by foguel

on measuring unboundedness of the h calculus for generators of analytic semigroups we investigate the boundedness of the h infty calculus by estimating the bound b e of the mapping h infty b x f f a t e for e near zero here a generates the analytic semigroup t and h infty is the space of bounded analytic functions on a domain strictly containing the spectrum of a we show that b e o loge in general whereas b e o 1 for bounded calculi this generalizes a result by vitse and complements work by haase and rozendaal for non analytic semigroups we discuss the sharpness of our bounds and show that single square function estimates yield b e o loge

asymptotics for periodic systems abstract this paper investigates the asymptotic behaviour of solutions of periodic evolution equations starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications for this class of systems we analyse in detail the spectral properties of the associated monodromy operator showing in particular that it is a so called ritt operator under a natural resonance condition this allows us to deduce from our general result a precise description of the asymptotic behaviour of the corresponding solutions in particular we present conditions for rational rates of convergence to periodic solutions in the case where the convergence fails to be uniformly exponential we illustrate our general results by applying them to concrete problems including the one dimensional wave equation with periodic damping

tauberian theorems for the laplace stieltjes transform let a 0 oo c be a function of locally bounded variation with a 0 0 whose laplace stieltjes transform g z fo e z da t is absolutely convergent for re z 0 let e be the singular set of g in ir and suppose that 0 e various estimates for lim supt la t g o l are obtained in particular a t g 0 as t oo if i e is null ii sup sup e aysda s oo yee t o o iii lim lim sup sup a s a t 0 610 t oo t 6 s t this result contains tauberian theorems for laplace transforms power series and dirichlet series

herstein s theorems and simplicity of hermitian jordan systems abstract in this paper we extend herstein s first construction relating associative and jordan ideals to pairs and triple systems as a consequence we show that an associative pair or triple system is simple if and only if its jordan symmetrization is simple we also generalize herstein s second construction to ample subsystems of associative algebras pairs and triple systems which provides information on their simplicity when the associative structure is simple

stability of the method of lines it is well known that a necessary condition for the lax stability of the method of lines is that the eigenvalues of the spatial discretization operator scaled by the time stepk lie within a distanceo k of the stability region of the time integration formula ask 0 in this paper we show that a necessary and sufficient condition for stability except for an algebraic factor is that the pseudo eigenvalues of the same operator lie within a distanceo o k of the stability region ask 0 our results generalize those of an earlier paper by considering a runge kutta and other one step formulas b implicit as well as explicit linear multistep formulas c weighted norms d algebraic stability e finite and infinite time intervals and f stability regions with cusps in summary the theory presented in this paper amounts to a transplantation of the kreiss matrix theorem from the unit disk for simple power iterations to an arbitrary stability region for method of lines calculations

about the sharpness of the stability estimates in the kreiss matrix theorem one of the conditions in the kreiss matrix theorem involves the resolvent of the matrices a under consideration this so called resolvent condition is known to imply for all n 1 the upper bounds an ek n 1 and an ek n 1 here is the spectral norm k is the constant occurring in the resolvent condition and the order of a is equal to n 1 1 it is a long standing problem whether these upper bounds can be sharpened for all fixed k 1 to bounds in which the right hand members grow much slower than linearly with n 1 and with n 1 respectively in this paper it is shown that such a sharpening is impossible the following result is proved for each e 0 there are fixed values c 0 k 1 and a sequence of n 1 n 1 matrices an satisfyirig the resolvent condition such that an n c n 1 1 e c n 1 1 e for n n 1 2 3 the result proved in this paper is also relevant to matrices a whose e pseudospectra lie at a distance not exceeding ke from the unit disk for all e 0

extremal growth of powers of operators satisfying resolvent conditions of kreiss ritt type let e be a compact subset of the unit circle we determine the extremal rate of growth of tn n 1 for banach space operators t satisfying the resolvent condition t i 1 const dist e 1 this includes as extreme cases the kreiss condition e t and the ritt condition e 1 for intermediate sets e the cardinality the measure and the hausdorff dimension of e all play a role in determining the growth of tn as a by product we also obtain lower bounds for the taylor coefficients of functions f holomorphic on the unit disk and satisfying f z 1dist z e z 1

resolvent conditions and bounds on the powers of matrices with relevance to numerical stability of initial value problems we deal with the problem of establishing upper bounds for the norm of the nth power of square matrices this problem is of central importance in the stability analysis of numerical methods for solving linear initial value problems for ordinary partial or delay differential equations a review is presented of upper bounds which were obtained in the literature under the resolvent condition occurring in the kreiss matrix theorem as well as under variants of that condition moreover we prove new bounds under resolvent conditions which generalize some of the reviewed ones the paper concludes by applying one of the new upper bounds in a stability analysis of the trapezoidal rule for delay differential equations

associative systems generated by symmetric elements of a system with involution abstract in this paper we study associative systems algebras pairs or triples with involution and we extend to them well known results of herstein see for example 5 in particular we show that any simple associative algebra is either generated by traces or it is a composition algebra for some involution in the case of simple associative pairs or triple systems they are either generated by traces or their sets of symmetric elements satisfy a certain clifford homotope pi moreover we show that the associative subpair generated by any ample subspace inherits regularity conditions such as primeness simplicity and primitivity from an associative pair and that the baer properly nilpotent locally nilpotent and jacobson radicals of the associative subpair generated by any ample subspace are directly inherited from the same radical of the whole pair we end up with a close description of ample subspaces for simple algebras pairs or triple systems generated by traces

resolvent criteria for similarity to a normal operator with spectrum on a curve abstract we give some new criteria for a hilbert space operator with spectrum on a smooth curve to be similar to a normal operator in terms of pointwise and integral estimates of the resolvent these results generalize criteria of stampfli van casteren and naboko and answers several questions posed by stampfli in 48 the main tools are from our recent results 12 on dilation to the boundary of the spectrum along with the dynkin functional calculus for smooth functions which is based on pseudoanalytic continuation

power boundedness in fourier and fourier stieltjes algebras and other commutative banach algebras abstract we study power boundedness in the fourier and fourier stieltjes algebras a g and b g of a locally compact group g as well as in some other commutative banach algebras the main results concern the question of when all elements with spectral radius at most one in any of these algebras are power bounded the characterization of power bounded elements in a g and b g and also the structure of the gelfand transform of a single power bounded element

on power bounded operators abstract the main result asserts that for any contraction t on an arbitrary banach space x t n t n 1 0 as n if and only if the spectrum of t has no points on the unit circle except perhaps z 1 this theorem is extended for t t n where is a function of spectral synthesis on the unit circle as an application we generalize the so called zero two law of ornstein and sucheston and zaharopol to positive contraction on a very large class of banach lattices

ratio limit theorems and tauberian theorems for vector valued functions and sequences abstract we prove ratio limit theorems for c means 0 and abel means of functions and sequences in banach spaces and ratio tauberian theorems for c means 1 and abel means of functions and sequences in banach lattices

ergodic and dynamical properties of m isometries abstract an example of a weakly ergodic 3 isometry is provided in 3 we give new examples of weakly ergodic 3 isometries and study numerically hypercyclic m isometries on finite and infinite dimensional hilbert spaces in particular all weakly ergodic strict 3 isometries on a hilbert space are weakly numerically hypercyclic adjoints of unilateral forward weighted shifts which are strict m isometries on l 2 n are shown to be hypercyclic

tauberian theorems and stability of solutions of the cauchy problem let f r x be a bounded strongly measurable function with values in a banach space x and let ie be the singular set of the laplace transform f in ir suppose that e is countable and 0 e i uf s u du 0 uniformly for s 0 as 0 for each in e it is shown that t 0 e i uf u du f i 0 as t for each in r e in particular f t 0 if f is uniformly continuous this result is similar to a tauberian theorem of arendt and batty it is obtained by applying a result of the authors concerning local stability of bounded semigroups to the translation semigroup on buc r x and it implies several results concerning stability of solutions of cauchy problems

stability estimates for families of matrices of nonuniformly bounded order this paper addresses the problem of establishing upper bounds for the norm of the nth power of square matrices the focus is on upper bounds that are valid for families of matrices of finite but nonuniformly bounded order such upper bounds are relevant to the stability analysis of numerical methods for solving differential equations in the famous kreiss matrix theorem a condition on the resolvent of matrices occurs which implies that the norm of the nth power does not grow faster than linearly with n in this paper a slightly stronger version of this resolvent condition is studied which is often satisfied in cases of practical interest we prove that this version implies growth at a rate that is essentially lower than in the case of the classical kreiss resolvent condition we consider also a condition on the iterated resolvent of matrices which is related to one of the assumptions occurring in the hille yosida theorem this condition is known to imply growth at a rate b n we prove that when a slightly stronger version of the iterated resolvent condition is in force there is growth at a rate that is at most n 1 1 with 0 q p i

resolvent conditions and growth of powers of operators abstract following bermudez et al 5 we study the rate of growth of the norms of the powers of a linear operator under various resolvent conditions or cesaro boundedness assumptions in hilbert spaces we prove that if t satisfies the kreiss condition t n o n log n if t is absolutely cesaro bounded t n o n 1 2 e for some e 0 which depends on t if t is strongly kreiss bounded then t n o log n for some 0 we show that a kreiss bounded operator on a reflexive space is abel ergodic and its cesaro means of order converge strongly when 1

optimal rates of decay in the katznelson tzafriri theorem for operators on hilbert spaces abstract the katznelson tzafriri theorem is a central result in the asymptotic theory of discrete operator semigroups it states that for a power bounded operator t on a banach space we have t n i t 0 if and only if t t 1 the main result of the present paper gives a sharp estimate for the rate at which this decay occurs for operators on hilbert space assuming the growth of the resolvent norms r e i t as 0 satisfies a mild regularity condition this significantly extends an earlier result by the second author which covered the important case of polynomial resolvent growth we further show that under a natural additional assumption our condition on the resolvent growth is not only sufficient but also necessary for the conclusion of our main result to hold by considering a suitable class of toeplitz operators we show that our theory has natural applications even beyond the setting of normal operators for which we in addition obtain a more general result

cesaro means and the kreiss matrix theorem abstract we present some new equivalent conditions in the kreiss matrix theorem involving higher order cesaro means these are interesting for the issue of treating families of matrices with no bound on the dimensions