the bishop phelps bollobas version of lindenstrauss properties a and b we study a bishop phelps bollobas version of lindenstrauss properties a and b for domain spaces we study banach spaces x such that x y has the bishopphelps bollobas property bpbp for every banach space y we show that in this case there exists a universal function x e such that for every y the pair x y has the bpbp with this function this allows us to prove some necessary isometric conditions for x to have the property we also prove that if x has this property in every equivalent norm then x is one dimensional for range spaces we study banach spaces y such that x y has the bishop phelps bollobas property for every banach space x in this case we show that there is a universal function y e such that for every x the pair x y has the bpbp with this function this implies that this property of y is strictly stronger than lindenstrauss property b the main tool to get these results is the study of the bishop phelps bollobas property for c0 1and sums of banach spaces

a bishop phelps bollobas type theorem for uniform algebras abstract this paper is devoted to showing that asplund operators with range in a uniform banach algebra have the bishop phelps bollobas property i e they are approximated by norm attaining asplund operators at the same time that a point where the approximated operator almost attains its norm is approximated by a point at which the approximating operator attains it to prove this result we use the weak to norm fragmentability of weak compact subsets of the dual of asplund spaces and we need to observe a urysohn type result producing peak complex valued functions in uniform algebras that are small outside a given open set and whose image is inside a stolz region

characterization of banach spaces y satisfying that the pair l 4 y has the bishop phelps bollobas property for operators abstract we study the bishop phelps bollobas property for operators from l 4 to a banach space for this reason we introduce an appropriate geometric property namely the ahsp l 4 we prove that spaces y satisfying ahsp l 4 are precisely those spaces y such that l 4 y has the bishop phelps bollobas property we also provide classes of banach spaces satisfying this condition for instance finite dimensional spaces uniformly convex spaces c 0 l and l 1 satisfy ahsp l 4

the bishop phelps bollobas theorem for operators we prove the bishop phelps bollobas theorem for operators from an arbitrary banach space x into a banach space y whenever the range space has property of lindenstrauss we also characterize those banach spaces y for which the bishop phelps bollobas theorem holds for operators from 1 into y s everal examples of classes of such spaces are provided for instance the bishop phelps bollobas theorem holds when the range space is finite dimensional an l1 space for a finite measure a c k space for a compact hausdorff space k or a uniformly convex banach space

comparison theorems in hereditary structures and applications abstract in this paper some new comparison theorems between lower solutions and upper solutions in the caratheodory sense of functional cauchy problems are established criteria on continuous dependence and a functional extension of muller s theorem are derived as applications

bishop phelps bollobas property for certain spaces of operators abstract we characterize the banach spaces y for which certain subspaces of operators from l 1 into y have the bishop phelps bollobas property in terms of a geometric property of y namely ahsp this characterization applies to the spaces of compact and weakly compact operators new examples of banach spaces y with ahsp are provided we also obtain that certain ideals of asplund operators satisfy the bishop phelps bollobas property

existence uniqueness and continuous dependence for hereditary differential equations abstract in the setting of functional differential equations an abstract hereditary structure is introduced which includes and unifies many formulations already considered by other authors for the new structure existence uniqueness and continuous dependence theorems are given

numerical computation of normal forms around some periodic orbits of the restricted three body problem in this paper we introduce a general methodology for computing numerically the normal form around a periodic orbit of an autonomous analytic hamiltonian system the process follows two steps first we expand the hamiltonian in suitable coordinates around the orbit and second we perform a standard normal form scheme based on the lie series method this scheme is carried out up to some finite order and neglecting the remainder we obtain an accurate description of the dynamics in a small enough neighbourhood of the orbit in particular we obtain the invariant tori that generalize the elliptic directions of the periodic orbit on the other hand bounding the remainder one obtains lower estimates for the diffusion time around the orbit this procedure is applied to an elliptic periodic orbit of the spatial restricted three body problem the selected orbit belongs to the lyapunov family associated to the vertical oscillation of the equilibrium point l 5 the mass parameter mu has been chosen such that l 5 is unstable but the periodic orbit is still stable this allows to show the existence of regions of effective stability near l 5 for values of mu bigger that the routh critical value the computations have been done using formal expansions with numerical coefficients

geometry of the ergodic quotient reveals coherent structures in flows abstract dynamical systems that exhibit diverse behaviors can rarely be completely understood using a single approach however by identifying coherent structures in their state spaces i e regions of uniform and simpler behavior we could hope to study each of the structures separately and then form the understanding of the system as a whole the method we present in this paper uses trajectory averages of scalar functions on the state space to a identify invariant sets in the state space and b to form coherent structures by aggregating invariant sets that are similar across multiple spatial scales first we construct the ergodic quotient the object obtained by mapping trajectories to the space of the trajectory averages of a function basis on the state space second we endow the ergodic quotient with a metric structure that successfully captures how similar the invariant sets are in the state space finally we parametrize the ergodic quotient using intrinsic diffusion modes on it by segmenting the ergodic quotient based on the diffusion modes we extract coherent features in the state space of the dynamical system the algorithm is validated by analyzing the arnold beltrami childress flow which was the test bed for alternative approaches the ulam s approximation of the transfer operator and the computation of lagrangian coherent structures furthermore we explain how the method extends the poincare map analysis for periodic flows as a demonstration we apply the method to a periodically driven three dimensional hill s vortex flow discovering unknown coherent structures in its state space finally we discuss differences between the ergodic quotient and alternatives propose a generalization to analysis of quasi periodic structures and lay out future research directions

the bishop phelps bollobas theorem for l l1 μ l 0 1 abstract we show that the bishop phelps bollobas theorem holds for all bounded operators from l 1 into l 0 1 where is a finite measure

simultaneously continuous retraction and bishop phelps bollobas type theorem abstract the dual space x of a banach space x is said to admit a uniformly simultaneously continuous retraction if there is a retraction r from x onto its unit ball b x which is uniformly continuous in norm topology and continuous in weak topology we prove that if a banach space resp complex banach space x has a normalized unconditional schauder basis with unconditional basis constant 1 and if x is uniformly monotone resp uniformly complex convex then x admits a uniformly simultaneously continuous retraction it is also shown that x admits such a retraction if x x i c 0 or x x i l 1 where x i is a family of separable banach spaces whose duals are uniformly convex with moduli of convexity i e with inf i i e 0 for all 0 e 1 let k be a locally compact hausdorff space and let c 0 k be the real banach space consisting of all real valued continuous functions vanishing at infinity as an application of simultaneously continuous retractions we show that a pair x c 0 k has the bishop phelps bollobas property for operators if x admits a uniformly simultaneously continuous retraction as a corollary c 0 s c 0 k has the bishop phelps bollobas property for operators for every locally compact metric space s

the bishop phelps bollobas theorem for operators from l1 sums of banach spaces abstract we introduce a generalized approximate hyperplane series property for a pair x y of banach spaces to characterize when l 1 x y has the bishop phelps bollobas property in particular we show that x y has this property if x y are finite dimensional if x is a c k space and y is a hilbert space or if x is asplund and y c 0 l where k is a compact hausdorff space and l is a locally compact hausdorff space

fractal weyl law behavior in an open hamiltonian system we numerically show fractal weyl law behavior in an open hamiltonian system that is described by a smooth potential and which supports numerous above barrier resonances this behavior holds even relatively far away from the classical limit the complex resonance wave functions are found to be localized on the fractal classical repeller

the bishop phelps bollobas property for operators from c k to uniformly convex spaces abstract we show that the pair c k x has the bishop phelps bollobas property for operators if k is a compact hausdorff space and x is a uniformly convex space

equivalence of different hereditary structures in ordinary differential equations abstract we prove that different formulations of hereditary settings for ordinary differential systems which appeared not comparable are actually equivalent

superexponential stability of kam tori we study the dynamics in the neighborhood of an invariant torus of a nearly integrable system we provide an upper bound to the diffusion speed which turns out to be of superexponentially small size exp exp 1 being the distance from the invariant torus we also discuss the connection of this result with the existence of many invariant tori close to the considered one

fraisse limits in functional analysis we provide a unified approach to fraisse limits in functional analysis including the gurarij space the poulsen simplex and their noncommutative analogs we obtain in this general framework many known and new results about the gurarij space and the poulsen simplex and at the same time establish their noncommutative analogs particularly we construct noncommutative analogs of universal operators in the sense of rota

stability of motions near resonances in quasi integrable hamiltonian systems nekhoroshev s theorem on the stability of motions in quasi integrable hamiltonian systems is revisited at variance with the proofs already available in the literature we explicitly consider the case of weakly perturbed harmonic oscillators furthermore we prove the confinement of orbits in resonant regions in the general case of nonisochronous systems by using the elementary idea of energy conservation instead of more complicated mechanisms an application of nekhoroshev s theorem to the study of perturbed motions inside resonances is also provided

the bishop phelps bollobas theorem for operators from l1 μ to banach spaces with the radon nikodým property abstract let y be a banach space and be a finite measure space where is an infinite algebra of measurable subsets of we show that if the couple l 1 y has the bishop phelps bollobas property for operators then y has the ahsp further for a banach space y with the radon nikod m property we prove that the couple l 1 y has the bishop phelps bollobas property for operators if and only if y has the ahsp

some geometric properties of disk algebras abstract in this paper we study some geometrical properties of certain classes of uniform algebras in particular the ball algebra a u b x of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex banach space x we prove that a u b x has k numerical index 1 for every k the lushness and also the ahsp moreover the disk algebra a d and more in general any uniform algebra whose choquet boundary has no isolated points is proved to have the polynomial daugavet property most of those properties are extended to the vector valued version a x of a uniform algebra a

on the intrinsic and the spatial numerical range for a bounded function f from the unit sphere of a closed subspace x of a banach space y w e study when the closed convex hull of its spatial numerical range w f is equal to its intrinsic numerical range v f we show that for every infinite dimensional banach space x there is a superspace y and a bounded linear operator t x y such that co w t v t we also show that up to renormig for every non reflexive banach space y one can find a closed subspace x and a bounded linear operator t l x y such that co w t v t finally we introduce a sufficient condition for the closed convex hull of the spatial numerical range to be equal to the intrinsic numerical range which we call the bishop phelps bollobas property and which is weaker than the uniform smoothness and the finite dimensionality we characterize strong subdifferentiability and uniform smoothness in terms of this property

effective stability for a hamiltonian system near an elliptic equilibrium point with an application to the restricted three body problem abstract we consider an n degrees of freedom hamiltonian system near an elliptic equilibrium point the system is put in normal form up to an arbitrary order and with respect to some resonance module and estimates are obtained for both the size of the remainder and for the domain of convergence of the transformation leading to normal form a bound to the rate of diffusion is thus found and by optimizing the order of normalization exponential estimates of nekhoroshev s type are obtained this provides explicit estimates for the stability properties of the elliptic point and leads in some cases to effective stability i e stability up to finite but long times an application to the stability of the triangular libration points in the spatial restricted three body is also given

near invariant tori on exponentially long time for poisson systems this paper deals with the near invariant tori for poisson systems it is shown that the orbits with the initial points near the diophantine torus approach some quasi periodic orbits over an extremely long time in particular the results hold for the classical hamiltonian system and in this case the drift of the motions is smaller than the one in the past works

operators on separable l1 predual spaces abstract we give an extension of the classical bartle dunford schwartz theorem for weakly compact operators on a c k space to weakly compact operators on a separable l 1 predual space using this we show that for operators on these spaces the set of weakly compact operators that attain their norm is dense in the space of weakly compact operators for operators from the space of affine continuous functions on a metrizable choquet simplex with values in an uniformly convex space we show that the operator theoretic version of the bishop phelps bollobas property is valid this gives an extension of some recent work of kim and lee

the bishop phelps bollobas theorem for operators on l1 μ in this paper we show that the bishop phelps bollobas theorem holds for l l1 l1 for all measures and and also holds for l l1 l for every arbitrary measure and every localizable measure finally we show that the bishop phelps bollobas theorem holds for two classes of bounded linear operators from a real l1 into a real c k if is a finite measure and k is a compact hausdorff space in particular one of the classes includes all bochner representable operators and all weakly compact operators

the bishop phelps bollobas property and lush spaces abstract we prove that for every lush space x the couple l 1 x has the bishop phelps bollobas property for operators that is every lush space has the ahsp standing for the approximate hyperplane series property while every lush space has the alternative daugavet property there exists a space with the alternative daugavet property that does not have the ahsp we also show that there is a banach space with both the ahsp and the alternative daugavet property which is not lush

on banach spaces whose group of isometries acts micro transitively on the unit sphere abstract we study banach spaces whose group of isometries acts micro transitively on the unit sphere we introduce a weaker property inherited by one complemented subspaces that we call uniform micro semitransitivity we prove a number of results about both micro transitive and uniformly micro semitransitive spaces in particular they are uniformly convex and uniformly smooth and form a self dual class to this end we relate the fact that the group of isometries acts micro transitively with a property of operators called the pointwise bishop phelps bollobas property and use some known results on it besides we show that if there is a non hilbertian non separable banach space with uniform micro semitransitive or micro transitive norm then there is a non hilbertian separable one finally we show that an l p space is micro transitive or uniformly micro semitransitive only when p 2

bishop phelps bollobas property for bilinear forms on spaces of continuous functions it is shown that the bishop phelps bollobas theorem holds for bilinear forms on the complex c 0 l 1 times c 0 l 2 for arbitrary locally compact topological hausdorff spaces l 1 and l 2

the bishop phelps bollobas property for lipschitz maps abstract in this paper we introduce and study a lipschitz version of the bishop phelps bollobas property lip bpb property this property deals with the possibility of making a uniformly simultaneous approximation of a lipschitz map f and a pair of points at which f almost attains its norm by a lipschitz map g and a pair of points such that g strongly attains its norm at the new pair of points we first show that if m is a finite pointed metric space and y is a finite dimensional banach space then the pair m y has the lip bpb property and that both finiteness assumptions are needed next we show that if m is a uniformly gromov concave pointed metric space i e the molecules of m form a set of uniformly strongly exposed points then m y has the lip bpb property for every banach space y we further prove that this is the case for finite concave metric spaces ultrametric spaces and holder metric spaces the extension of the lip bpb property from m r to some banach spaces y and some results for compact lipschitz maps are also discussed

effective stability and kam theory abstract the two main stability results for nearly integrable hamiltonian systems are revisited nekhoroshev theorem concerning exponential lower bounds for the stability time effective stability and kam theorem concerning the preservation of a majority of the nonresonant invariant tori perpetual stability to stress the relationship between both theorems a common approach is given to their proof consisting of bringing the system to a normal form constructed through the lie series method the estimates obtained for the size of the remainder rely on bounds of the associated vectorfields allowing one to get the optimal stability exponent in nekhoroshev theorem for quasiconvex systems on the other hand a direct and complete proof of the isoenergetic kam theorem is obtained moreover a modification of the proof leads to the notion of nearly invariant torus which constitutes a bridge between kam and nekhoroshev theorems

facial characterizations of complex lindenstrauss spaces we characterize complex banach spaces a whose banach dual spaces are l 1 spaces in terms of l ideals generated by certain extremal subsets of the closed unit ball k of a our treatment covers the case of spaces a containing constant functions and also spaces not containing constants separable spaces are characterized in terms of w compact sets of extreme points of k whereas the nonseparable spaces necessitate usage of the w closed faces of k our results represent natural extensions of known characterizations of choquet simplexes we obtain also a characterization of complex lindenstrauss spaces in terms of boundary annihilating measures and this leads to a characterization of the closed subalgebras of c c x which are complex lindenstrauss spaces

the bishop phelps bollobas property for operators between spaces of continuous functions abstract we show that the space of bounded linear operators between spaces of continuous functions on compact hausdorff topological spaces has the bishop phelps bollobas property a similar result is also proved for the class of compact operators from the space of continuous functions vanishing at infinity on a locally compact and hausdorff topological space into a uniformly convex space and for the class of compact operators from a banach space into a predual of an l 1 space

kam tori are very sticky rigorous lower bounds on the time to move away from an invariant lagrangian torus with linear flow abstract hamiltonian perturbation theory is used to derive rigorous nekhoroshev type lower bounds on the time it takes to move away from an invariant lagrangian torus when the flow on the torus is conjugate to a highly non resonant linear flow in particular these results give bounds on the time to move away from a kam torus if r is the distance from the torus then the lower bound on the time to double the distance from the torus is c r e k r where c and k are constants 1 n 2 n is the number of degrees of freedom and is a measure of the irrationality of the flow we thus prove that nearby trajectories take an extremely long time to move away from such an invariant torus and that the more irrational the linear flow the stickier the torus will be these estimates do not require the steepness or quasi convexity assumptions of nekherosev s theorem