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

a urysohn type theorem and the bishop phelps bollobas theorem for holomorphic functions abstract a urysohn type theorem is introduced for a subalgebra of the algebra c b of all bounded complex valued continuous functions on a hausdorff topological space with use of this theorem it is shown that a type of the bishop phelps bollobas theorem holds for certain classes of holomorphic functions on the unit ball of a complex banach space x if x is either a locally uniformly convex space or a locally c uniformly convex order continuous sequence space

emerging notions of norm attainment for lipschitz maps between banach spaces abstract we classify several notions of norm attaining lipschitz maps which were introduced previously and present the relations among them in order to verify proper inclusions we also analyze some results for the sets of lipschitz maps satisfying each of these properties to be dense or not in lip 0 x y for instance we characterize a banach space y with the radon nikod m property in terms of the denseness of norm attaining lipschitz maps with values in y further we introduce a property called the local directional bishop phelps bollobas property for lipschitz compact maps which extends the one studied previously for scalar valued functions and provide some new positive results

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

γ flatness and bishop phelps bollobas type theorems for operators the bishop phelps bollobas property deals with simultaneous approximation of an operator t and a vector x at which t nearly attains its norm by an operator t 0 t 0 and a vector x 0 x 0 respectively such that t 0 t 0 attains its norm at x 0 x 0 in this note we extend the already known results about the bishop phelps bollobas property for asplund operators to a wider class of banach spaces and to a wider class of operators instead of proving a bpb type theorem for each space separately we isolate two main notions flat operators and banach spaces with ack ack structure in particular we prove a general bpb type theorem for flat operators acting to a space with ack ack structure and show that uniform algebras and spaces with the property have ack ack structure we also study the stability of the ack ack structure under some natural banach space theory operations as a consequence we discover many new examples of spaces y such that the bishop phelps bollobas property for asplund operators is valid for all pairs of the form x y x y

a characterization of certain griesmer codes mmd codes in a more general sense let c be an n k d sub q linear code the defect of c is the parameter s s c n k 1 d if k spl ges m 1 spl ges 2 then by the griesmer bound d spl les q sup m q 1 q sub m 1 s m the author s interest is in those linear codes having the maximum minimum distance i e d q sup m q 1 q sup m 1 s m for m 1 we have d q s 1 and the codes are maximum minimum distance mmd codes in the sense of faldum and willems see ibid vol 44 p 1555 58 1998 thus we consider mmd codes in a more general sense we refer to them simply as mmd codes all mmd codes with m 1 are known up to formal equivalence note that two codes are formally equivalent if they have the same weight distribution the author classifies up to formal equivalence the mmd codes with m spl ges 2

local bishop phelps bollobas properties abstract in this paper we introduce some local versions of bishop phelps bollobas type property for operators that is the function which appears in their definitions depends not only on a given e 0 but also on either a fixed norm one operator t or a fixed norm one vector x we investigate those properties and show differences between local and uniform versions

the duals of mmd codes are proper for error detection a linear code when used for error detection on a symmetric channel is said to be proper if the corresponding undetected error probability increases monotonically in spl epsiv the symbol error probability of the channel such codes are generally considered to perform well in error detection a number of well known classes of linear codes are proper e g the perfect codes mds codes macdonald s codes mmd codes and some near mds codes the aim of this work is to show that also the duals of mmd codes are proper

multiple summing operators on banach spaces abstract in this paper we improve some previous results about multiple p summing multilinear operators by showing that every multilinear form from l 1 spaces is multiple p summing for 1 p 2 the proof is based on the existence of a predual for the banach space of multiple p summing multilinear forms we also show the failure of the inclusion theorem in this class of operators and improve some results of y melendez and a tonge about dominated multilinear operators

the mmd codes are proper for error detection the undetected error probability of a linear code used to detect errors on a symmetric channel is a function of the symbol error probability spl epsi of the channel and involves the weight distribution of the code the code is proper if the undetected error probability increases monotonously in spl epsi proper codes are generally considered to perform well in error detection we show in this correspondence that maximum minimum distance mmd codes are proper

some techniques on nonlinear analysis and applications in this paper we present two different results in the context of nonlinear analysis the first one is essentially a nonlinear technique that in view of its strong generality may be useful in different practical problems the second result more technical but also connected to the first one is an extension of the well known pietsch domination theorem the last decade witnessed the birth of different families of pietsch domination type results and some attempts of unification our result that we call full general pietsch domination theorem is potentially a definitive pietsch domination theorem which unifies the previous versions and delimits what can be proved in this line the connections to the recent notion of weighted summability are traced

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

norm or numerical radius attaining polynomials on c k abstract let c k c be the banach space of all complex valued continuous functions on a compact hausdorff space k we study when the following statement holds every norm attaining n homogeneous complex polynomial on c k c attains its norm at extreme points we prove that this property is true whenever k is a compact hausdorff space of dimension less than or equal to one in the case of a compact metric space a characterization is obtained as a consequence we show that for a scattered compact hausdorff space k every continuous n homogeneous complex polynomial on c k c can be approximated by norm attaining ones at extreme points and also that the set of all extreme points of the unit ball of c k c is a norming set for every continuous complex polynomial similar results can be obtained if norm is replaced by numerical radius

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

the bishop phelps bollobas theorem fails for bilinear forms on l1 l1 abstract in this paper we show that the bishop phelps bollobas theorem fails for bilinear forms on l 1 l 1 while it holds for linear operators from l 1 to l

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

a lindenstrauss theorem for some classes of multilinear mappings abstract under some natural hypotheses we show that if a multilinear mapping belongs to some banach multilinear ideal then it can be approximated by multilinear mappings belonging to the same ideal all whose arens extensions attain their norms at the same point we prove a similar result for the class of symmetric multilinear mappings we see that the quantitative bollobas type version of these results fails in every multilinear ideal

integral mappings between banach spaces abstract we consider the classes of grothendieck integral g integral and pietsch integral p integral linear and multilinear operators see definitions below and we prove that a multilinear operator between banach spaces is g integral resp p integral if and only if its linearization is g integral resp p integral on the injective tensor product of the spaces together with some related results concerning certain canonically associated linear operators as an application we give a new proof of a result on the radon nikodym property of the dual of the injective tensor product of banach spaces moreover we give a simple proof of a characterization of the g integral operators on c k x spaces and we also give a partial characterization of p integral operators on c k x spaces

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

the bishop phelps bollobas property for numerical radius on l1 abstract guirao and kozhushkina recently introduced the bishop phelps bollobas property for numerical radius geometrically speaking the bishop phelps bollobas property says that if we have a state and an operator that almost attains its numerical radius at this state then there exist another state close to the original state and another operator close to the original operator such that the new operator attains its numerical radius at this new state in this paper we study the bishop phelps bollobas property for numerical radius in the context of the banach space of lebesgue integrable functions over the real line

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

extreme polynomials and multilinear forms onl1 abstract given a 2 homogeneous polynomialp x y ax2 by2 cxywith real coefficients let p rand p cdenote the norms ofpon the real and complex banach spacel21 respectively we show p r p c and obtain a sufficient and necessary condition on the coefficientsa b andcforpto have norm 1 applying these results we characterize extreme points of the unit ball of p 2l1 for the real banach spacel21and examine them for the complex banach spacel21 we apply them to find extreme points and strongly extreme points of the unit ball of p 2l1 and get an extremal 2 homogeneous polynomial onl1that is not an extreme point we also characterize extreme points and strongly extreme points of the unit ball of l ml1 or l ml1 0 1

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

the bishop phelps bollobas property for operators from c0 into some banach spaces abstract we exhibit a new class of banach spaces y such that the pair c 0 y has the bishop phelps bollobas property for operators this class contains uniformly convex banach spaces and spaces with the property of lindenstrauss we also provide new examples of spaces in this class

on the polynomial lindenstrauss theorem abstract under certain hypotheses on the banach space x we show that the set of n homogeneous polynomials from x to any dual space whose aron berner extensions are norm attaining is dense in the space of all continuous n homogeneous polynomials to this end we prove an integral formula for the duality between tensor products and polynomials we also exhibit examples of lorentz sequence spaces for which there is no polynomial bishop phelps theorem but our results apply finally we address quantitative versions in the sense of bollobas of these results

symmetric multilinear forms on hilbert spaces where do they attain their norm abstract we characterize the sets of norm one vectors x 1 x k in a hilbert space h such that there exists a k linear symmetric form attaining its norm at x 1 x k we prove that in the bilinear case any two vectors satisfy this property however for k 3 only collinear vectors satisfy this property in the complex case while in the real case this is equivalent to x 1 x k spanning a subspace of dimension at most 2 we use these results to obtain some applications to symmetric multilinear forms symmetric tensor products and the exposed points of the unit ball of l s h k

on the bishop phelps bollobas theorem for multilinear mappings abstract we study the bishop phelps bollobas property and the bishop phelps bollobas property for numerical radius our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases we characterize the pair l 1 x y to have the bpbp for bilinear forms and prove that on l 1 the numerical radius and the norm of a multilinear mapping are the same we also show that l 1 fails the bpbp nu for multilinear mappings although l 1 satisfies it in the operator case for every measure

technical communique on the klimushchev krasovskii theorem the klimushchev krasovskii theorem describes a sufficient condition for the asymptotic stability of singularly perturbed systems motivated by some subtle examples this note presents a new necessary and sufficient condition by imposing an additional assumption on the statement of the klimushchev krasovskii theorem this note also extends the main inertia theorem to singularly perturbed systems

the bishop phelps bollobas point property abstract in this article we study a version of the bishop phelps bollobas property we investigate a pair of banach spaces x y such that every operator from x into y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm in this case we say that such a pair has the bishop phelps bollobas point property bpbpp we characterize uniform smoothness in terms of bpbpp and we give some examples of pairs x y which have and fail this property some stability results are obtained about l 1 and l sums of banach spaces and we also study this property for bilinear mappings

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

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

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

hypercyclic convolution operators on frechet spaces of analytic functions a result of godefroy and shapiro states that the convolution operators on the space of entire functions on c n which are not multiples of identity are hypercyclic analogues of this result have appeared for some spaces of holomorphic functions on a banach space in this work we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators some known results come out as particular cases of this setting we also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the schatten von neumann class

two sided polynomial ideals on banach spaces abstract classes of homogeneous polynomials between banach spaces have been studied in the last three decades from the perspective of the stability with respect to the composition of a homogeneous polynomial with linear operators in an attempt to explore the underlying nonlinearity in a more consistent way and to bring the subject closer to its roots in complex analysis and also taking into account recent results in the field in this paper we propose the study of classes of homogeneous polynomials that are stable under the composition with homogeneous polynomials

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

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

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

a characterization of mmd codes let c be a linear n k d code over gf q with k spl ges 2 if s n k 1 d denotes the defect of c then by the griesmer bound d spl les s 1 q now for obvious reasons we are interested in codes of given defect s for which the minimum distance is maximal i e d s 1 q we classify up to formal equivalence all such linear codes over gf q remember that two codes over gf q are formally equivalent if they have the same weight distribution it turns out that for k spl ges 3 such codes exist only in dimension 3 and 4 with the ternary extended golay code the ternary dual golay code and the binary even weight code as exceptions in dimension 4 they are related to ovoids in pg 3 q except the binary extended hamming code and in dimension 3 to maximal arcs in pg 2 q

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

singular perturbation of strictly positive realness abstract the robustness of the strictly positive real spr condition of linear time invariant multi input multi output lti mimo singularly perturbed systems is examined a necessary and sufficient condition under which the full system is spr is proved this robustness result is an extension of the analysis for the popov kalman yakubovich lemma by v r saksena and p v kokotovic 7

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

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

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

norm attaining bilinear forms onl1 0 1 abstract we show that the set of norm attaining bilinear forms onl1 0 1 is not dense in the space of all continuous bilinear forms

singular perturbation of the popov kaiman yakubovich lemma absolute stability of linear time invariant single input single output lti siso singularly perturbed systems with a time varying feedback element is examined via the popov kalman yakubovich pky lemma if the reduced order slow subsystem is absolutely stable then so is the full system provided the parasitics are sufficiently fast and stable

a multilinear lindenstrauss theorem abstract we show that the set of n linear mappings on a product of n banach spaces such that all their arens extensions attain their norms at the same element is norm dense in the space of all bounded n linear mappings