inferences on the common coefficient of variation the coefficient of variation is often used as a measure of precision and reproducibility of data in medical and biological science this paper considers the problem of making inference about the common population coefficient of variation when it is a priori suspected that several independent samples are from populations with a common coefficient of variation the procedures for confidence interval estimation and hypothesis testing are developed based on the concepts of generalized variables the coverage properties of the proposed confidence intervals and type i errors of the proposed tests are evaluated by simulation the proposed methods are illustrated by a real life example

geometrical implications of certain infinite dimensional decompositions we investigate the connections between the global structure of a banach space i e the existence of certain finite and infinite dimensional de compositions and the geometrical properties of the closed convex bounded sub sets of such a space i e the existence of extremal and other topologically distin guished points the global structures of various supposedly pathological examples of banach spaces constructed by r c james turn out to be more universal than expected for instance james tree type resp james matrix type decompositions characterize banach spaces with the point of continuity property resp the radon nikodym property moreover the convex point of continuity property is stable under the formation of james infinitely branching tree type sums of infinite dimensional factors we also give several counterex amples to various questions relating some topological and geometrical concepts in banach spaces

the gamma generalized normal distribution a descriptor of sar imagery abstract we propose a new four parameter distribution for modeling synthetic aperture radar sar imagery named the gamma generalized normal ggn by combining the gamma and generalized normal distributions a mathematical characterization of the new distribution is provided by identifying the limiting behavior and by calculating the density and moment expansions the ggn model performance is evaluated on both synthetic and actual data and for that maximum likelihood estimation and random number generation are discussed the proposed distribution is compared with the beta generalized normal bgn distribution which has already shown to appropriately represent sar imagery the performance of these two distributions are measured by means of statistics which provide evidence that the ggn can outperform the bgn distribution in some contexts

types in the n adic tree and minimal analytic gaps abstract we develop some technical tools for the study of the record structure of the n adic tree and we give as an application the list of the nine minimal analytic gaps

causality analysis of neural connectivity critical examination of existing methods and advances of new methods granger causality gc is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience especially its counterpart in frequency domain spectral gc as well as other granger like causality measures have recently been applied to study causal interactions between brain areas in different frequency ranges during cognitive and perceptual tasks in this paper we show that 1 gc in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series and 2 spectral gc and other granger like causality measures have inherent shortcomings and or limitations because of the use of the transfer function or its inverse matrix and partial information of the linear regression model on the other hand we propose two novel causality measures in time and frequency domains for the linear regression model called new causality and new spectral causality respectively which are more reasonable and understandable than gc or granger like measures especially from one simple example we point out that in time domain both new causality and gc adopt the concept of proportion but they are defined on two different equations where one equation for gc is only part of the other for new causality thus the new causality is a natural extension of gc and has a sound conceptual theoretical basis and gc is not the desired causal influence at all by several examples we confirm that new causality measures have distinct advantages over gc or granger like measures finally we conduct event related potential causality analysis for a subject with intracranial depth electrodes undergoing evaluation for epilepsy surgery and show that in the frequency domain all measures reveal significant directional event related causality but the result from new spectral causality is consistent with event related time frequency power spectrum activity the spectral gc as well as other granger like measures are shown to generate misleading results the proposed new causality measures may have wide potential applications in economics and neuroscience

the aic criterion and symmetrizing the kullback leibler divergence the akaike information criterion aic is a widely used tool for model selection aic is derived as an asymptotically unbiased estimator of a function used for ranking candidate models which is a variant of the kullback leibler divergence between the true model and the approximating candidate model despite the kullback leibler s computational and theoretical advantages what can become inconvenient in model selection applications is their lack of symmetry simple examples can show that reversing the role of the arguments in the kullback leibler divergence can yield substantially different results in this paper three new functions for ranking candidate models are proposed these functions are constructed by symmetrizing the kullback leibler divergence between the true model and the approximating candidate model the operations used for symmetrizing are the average geometric and harmonic means it is found that the original aic criterion is an asymptotically unbiased estimator of these three different functions using one of these proposed ranking functions an example of new bias correction to aic is derived for univariate linear regression models a simulation study based on polynomial regression is provided to compare the different proposed ranking functions with aic and the new derived correction with aicc

interpolation banach lattices containing no isomorphic copies of c0 abstract this article is concerned with the question of when the banach lattices generated by the interpolation method of constants contain no isomorphic copies of c 0 for this we study the kothe dual spaces of banach lattices obtained by the methods of constants and means we find an explicit formula for the kothe dual of banach lattices generated by the means method with a mild restriction on the parameters we apply these results to describe a large class of banach lattices generated by the method of constants containing no subspaces isomorphic to c 0 moreover we present applications to the strict singularity of certain inclusion maps between banach sequence lattices

on the near differentiability property of banach spaces abstract let be a scalar measure of bounded variation on a compact metrizable abelian group g suppose that has the property that for any measure whose fourier stieltjes transform vanishes at the measure has radon nikod m derivative with respect to the haar measure on g then l pigno and s saeki showed that itself has radon nikod m derivative such property is not shared by vector measures in general we say that a banach space x has the near differentiability property if every x valued measure of bounded variation shares the above property we prove that banach spaces with the radon nikod m property have the near differentiability property while banach spaces with the near differentiability property enjoy the near radon nikod m property we also show that the banach spaces l 1 0 1 and l 1 h 0 1 have the near differentiability property lastly we show that banach spaces with the near differentiability property have type ii radon nikod m property whenever is a riesz subset of type 0 of g

model selection for multivariate regression in small samples we develop a small sample criterion aicc for selecting multivariate regression models this criterion adjusts the akaike information criterion to be an exact unbiased estimator for the expected kullback leibler information a small sample comparison shows that aicc provides better model order choices than other available model selection methods data from an agricultural experiment are analyzed

the analytic complete continuity property abstract we introduce the notion of the analytic complete continuity property of banach spaces we give different characterizations of this property we show that this property is different from known related properties such as the complete continuity property and the analytic radon nikod m property

new examples of c 0 saturated banach spaces for every p 1 an isomorphically polyhedral banach space ep is constructed which has an unconditional basis and does not embed isomorphically into a c k space for any countable and compact metric space k moreover ep admits a quotient isomorphic to lp

modified mixed tsirelson spaces we study the modified and boundedly modified mixed tsirelson spacestm fkn n n 1 andtm s fkn n n 1 respectively defined by a subsequence fkn of the sequence of schreier families fn these are reflexive asymptotic l1spaces with an unconditional basis ei ihaving the property that every sequence xi ni 1of normalized disjointly supported vectors contained in ei i nis equivalent to the basis of ln1 we show that if lim 1 nn 1 then the spacet fn n n 1 and its modified variationstm fn n n 1 ortm s fn n n 1 are totally incomparable by proving thatc0is finitely disjointly representable in every block subspace oft fn n n 1 next we present an example of a boundedly modified mixed tsirelson spacexm 1 u tm 1 fkn n n 1 which is arbitrarily distortable finally we construct a variation of the spacexm 1 uwhich is hereditarily indecomposable

an asymptotic test for the equality of coefficients of variation from k populations the coefficient of variation is often used as a guide of the repeatability of measurements in clinical trials and other medical work when possible one makes repeated measurements on a set of individuals to calculate the relative variability of the test with the understanding that a reliable clinical test should give similar results when repeated on the same patient there are times however when repeated measurements on the same patient are not possible under these circumstances to combine results from different clinical trials or test sites it is necessary to compare the coefficients of variation of several clinical trials using the work of miller we develop a general statistic for testing the hypothesis that the coefficients of variation are the same for k populations with unequal sample sizes this statistic is invariant under the choice of the order of the populations and is asymptotically chi 2 we provide an example using data from yang and hayglass we compare the size and the power of the test to that of bennett doornbos and dijkstra and a statistic based on hedges and olkin

disjointly homogeneous banach lattices and compact products of operators the notion of disjointly homogeneous banach lattice is introduced in these spaces every two disjoint sequences share equivalent subsequences it is proved that on this class of banach lattices the product of a regular am compact and a regular disjointly strictly singular operators is always a compact operator

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

applications of the theory of semi embeddings to banach space theory let x and y be banach spaces and t x y an injective bounded linear operator t is called a semi embedding if t maps the closed unit ball of x to a closed subset of y this concept was introduced by lotz peck and porta proc edinburgh math soc 22 1979 233 240 it is proved that if x semi embeds in y and x is separable then x has the radon nikodym property provided y does it is shown that if l1 semi embeds in y then y fails the schur property and contains a subspace isomorphic to l1 as a consequence of the proof it is shown that if x is a subspace of l1 either l1 embeds in x or l1 embeds in l1x the simpler result that l1 does not semi embed in c0 is treated separately this result is used to deduce the classic result of menchoff that there exists a singular probability measure on the circle with fourier coefficients vanishing at infinity some generalizations of the notion of semi embedding are given and several complements and open questions are discussed

decompositions of banach lattices into direct sums we consider the problem of decomposing a banach lattice z as a direct sum z x y where x and y are complemented subspaces satisfying a condition of incomparability e g every operator from y to x is strictly singular we treat both the atomic and nonatomic cases in particular we answer a question of wojtaszczyk by showing that l1 ffll2 has unique structure as a nonatomic banach lattice one of the most important problems in the theory of banach lattices which is still open is whether any complemented subspace of a banach lattice must be linearly isomorphic to a banach lattice the main difficulty seems to lie in the fact that most of the criteria for a banach space to be isomorphic to a lattice do not really distinguish between lattices and their complemented subspaces we do not actually treat this question in the present paper but rather consider the situation z x d3 y where z is a banach lattice and x and y two complemented subspaces which are assumed to satisfy different conditions that make them distinct in some or another sense this line of research was initiated by p wojtaszczyk 128 and also by i s edelstein and p wojtaszczyk 3 who proved that if z has a normalized unconditional basis zn n l i e it is a separable atomic lattice so that every linear operator from y into x is compact then zn n l splits into two disjoint parts which are respectively equivalent to bases of x and y in particular both x and y have unconditional bases the proof of this result is based on a fundamental theorem from 28 and 3 which is mentioned below as theorem a we give here a different proof which does not make use of theorem a but instead is based on a simple change of signs result from 2 which is described below as theorem b we also consider the case when the compactness assumption above is replaced by the total incomparability of x and y for which we prove a similar result provided x and y have unconditional bases unfortunately the most interesting case when every operator from y into x is assumed to be strictly singular which was raised as an open problem in 28 remains unsolved we conclude the section devoted to the atomic case with a simple theorem on block bases of a space with unconditional basis zn 1 whose span is complemented such a block basis splits into two disjoint parts the first equivalent to a subsequence of zn n received by the editors september 5 1986 1980 mathematics subject classification 1985 revision primary 46b30 46b15 secondary 46a40 this research was supported by grant no 84 00210 from the united states israel binational science foundation bsf jerusalem israel the research of the first author was also supported in part by nsf grant dms 8500938 the research of the second author was also supported in part by nsf grant dms 8601401 r 1987 american mathematical society ooo2 9947 87 1 00 25 per page

some characterizations of the analytic radon nikodým property in banach spaces the analytic radon nikod m property for a complex banach space x is characterized in several ways analogous to the common characterizations of the radon nikod m property for example the banach space x has the analytic radon nikod m property if and only if any operator from l1 to x that factors through l1h01 is representable the characterizations are used to study complemented subspaces of l1h01 and to define the analytic radon nikod m property for real banach spaces

non asplund banach spaces and operators let w and z be banach spaces such that z is separable and let r w z r w z be a continuous linear operator we study consequences of the adjoint operator r r having non separable range from our main technical result we obtain applications to the theory of basic sequences and the existence of universal operators for various classes of operators between banach spaces we also obtain an operator theoretic characterisation of separable banach spaces with non separable dual

operators on c 0 1 preserving copies of asymptotic l1 spaces given separable banach spaces x y z and a bounded linear operator t x y then t is said to preserve a copy of z provided that there exists a closed linear subspace e of x isomorphic to z and such that the restriction of t to e is an into isomorphism it is proved that every operator on c 0 1 which preserves a copy of an asymptotic l1 space also preserves a copy of c 0 1

the three space problem for l 1 we construct a subspace x of l1 such that x is an 1 sum of spaces isomorphic to 11 but such that l1 x does not contain a copy of l1 we also construct two banach spaces e1 e2 that do not contain a copy of li but such that e1 x e2 contains a copy of l1 moreover the projections this content downloaded from 207 46 13 150 on thu 28 jul 2016 05 31 04 utc all use subject to http about jstor org terms the three space problem for l 29 of li on each factor are one to one and the images of the unit ball of l1 are closed these examples settle questions of j lindenstrauss p pelczynski j bourgain and h p rosenthal equipe d analyse tour 46 u a au c n r s n0 754 universitt paris vi 4 place jussieu 75230 paris cedex 05 department of mathematics ohio state university 231 w 18th avenue columbus ohio 43210 this content downloaded from 207 46 13 150 on thu 28 jul 2016 05 31 04 utc all use subject to http about jstor org terms

subspace information criterion for nonquadratic regularizers model selection for sparse regressors nonquadratic regularizers in particular the l sub 1 norm regularizer can yield sparse solutions that generalize well in this work we propose the generalized subspace information criterion gsic that allows to predict the generalization error for this useful family of regularizers we show that under some technical assumptions gsic is an asymptotically unbiased estimator of the generalization error gsic is demonstrated to have a good performance in experiments with the l sub 1 norm regularizer as we compare with the network information criterion nic and cross validation in relatively large sample cases however in the small sample case gsic tends to fail to capture the optimal model due to its large variance therefore also a biased version of gsic is introduced which achieves reliable model selection in the relevant and challenging scenario of high dimensional data and few samples

hrf estimation in fmri data with an unknown drift matrix by iterative minimization of the kullback leibler divergence hemodynamic response function hrf estimation in noisy functional magnetic resonance imaging fmri plays an important role when investigating the temporal dynamic of a brain region response during activations nonparametric methods which allow more flexibility in the estimation by inferring the hrf at each time sample have provided improved performance in comparison to the parametric methods in this paper the mixed effects model is used to derive a new algorithm for nonparametric maximum likelihood hrf estimation in this model the random effect is used to better account for the variability of the drift contrary to the usual approaches the proposed algorithm has the benefit of considering an unknown and therefore flexible drift matrix this allows the effective representation of a broader class of drift signals and therefore the reduction of the error in approximating the drift component estimates of the hrf and the hyperparameters are derived by iterative minimization of the kullback leibler divergence between a model family of probability distributions defined using the mixed effects model and a desired family of probability distributions constrained to be concentrated on the observed data the performance of proposed method is demonstrated on simulated and real fmri data the latter originating from both event related and block design fmri experiments

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

operators on c k spaces preserving copies of schreier spaces it is proved that an operator t c k x k compact metrizable x a separable banach space for which the e szlenk index of t bx is greater than or equal to 1 is an isomorphism on a subspace of c k isomorphic to x the schreier space of order as a corollary one obtains that a complemented subspace of c k with szlenk index equal to 1 contains a subspace isomorphic to x

a banach space block finitely universal for monotone bases a reflexive banach space x with a basis ei is constructed having the property that every monotone basis is block finitely representable in each block basis of x

a density version of the halpern lauchli theorem abstract we prove a density version of the halpern lauchli theorem this settles in the affirmative a conjecture of r laver specifically let us say that a tree t is homogeneous if t has a unique root and there exists an integer b 2 such that every t t has exactly b immediate successors we show that for every d 1 and every tuple t 1 t d of homogeneous trees if d is a subset of the level product of t 1 t d satisfying lim sup n d t 1 n t d n t 1 n t d n 0 then there exist strong subtrees s 1 s d of t 1 t d having a common level set such that the level product of s 1 s d is a subset of d

new examples of c0 saturated banach spaces ii abstract for every banach space z with a shrinking unconditional basis satisfying an upper p estimate for some p 1 an isomorphically polyhedral banach space is constructed which has an unconditional basis and admits a quotient isomorphic to z it follows that reflexive banach spaces with an unconditional basis and non trivial type tsirelson s original space and c 0 l p for p 1 are isomorphic to quotients of isomorphically polyhedral banach spaces with unconditional bases

ramsey families of subtrees of the dyadic tree we show that for every rooted finitely branching pruned tree t of height w there exists a family f which consists of order isomorphic to t subtrees of the dyadic tree c 0 1 n with the following properties i the family f is a g subset of 2 c ii every perfect subtree of c contains a member of f iii if k is an analytic subset of f then for every perfect subtree s of c there exists a perfect subtree s of s such that the set a f a c s either is contained in or is disjoint from k

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

use of renyi s divergence to test for the equality of the coefficients of variation a new family of test statistics based on renyi s divergence is introduced for the hypothesis that the coefficients of variation of k normal populations are equal a comparative simulation study is carried out concerning the size and power of these test statistics and earlier ones finally two members of the new family of tests emerge as the best from the simulation study

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

on the structure of non weakly compact operators on banach lattices in this paper we study extensions of theorems of hagler and stegall on lp spaces 11 and of rosenthal 24 25 and pelczynski 21 on c k spaces to more general banach spaces with some lattice structure which do not contain complemented copies of i r we show that i fx is a separable banach space such that co does not embed into x and t is a bounded linear operator from x into some banach space y such that t y is not separable then i if x has local unconditional structure h la gordon and lewis 7

banach lattice versions of strict singularity abstract we explore the relation between lattice versions of strict singularity for operators from a banach lattice to a banach space in particular we study when the class of disjointly strictly singular operators those not invertible on the span of any disjoint sequence coincides with that of lattice strictly singular operators i e those not invertible on any infinite dimensional sublattice new results are given which help to clarify the existing relation between these two classes

proximity to l1and distortion in asymptotic l1spaces abstract for an asymptotic l 1 space x with a basis x i certain asymptotic l 1 constants x are defined for 1 x measures the equivalence between all normalized block bases y i k i 1 of x i which are s admissible with respect to x i s is the th schreier class of sets and the unit vector basis of l k 1 this leads to the concept of the delta spectrum of x x which reflects the behavior of stabilized limits of x the analogues of these constants under all renormings of x are also defined and studied we investigate x both in general and for spaces of bounded distortion we also prove several results on distorting the classical tsirelson s space t and its relatives

radon nikodým properties associated with subsets of countable discrete abelian groups with any subset of a countable discrete abelian we associate with it three banach space properties these properties are radon nikodym type properties the relationship between these properties is investigated the results are applied to give new characterizations of riesz subsets and rosenthal subsets of countable discrete abelian groups

gδ embeddings in hilbert space abstract it is shown that a separable banach space x has the point of weak to norm continuity property resp the radon nikodym property if and only if there exists a compact g embedding resp an h embedding from x into l2 this solves several questions of j bourgain and h p rosenthal j funct anal 52 1983 it is also shown that every non relatively compact sequence in a banach space with property pc has a difference subsequence which is a boundedly complete basic sequence this solves a question of pelczynski and extends some results of w b johnson and h p rosenthal studia math 43 1972 77 92 various related questions asked in the above bourgain rosenthal reference and by g a edgar and r f wheeler pac j math 115 1984 and n ghoussoub and h p rosenthal math ann 264 1983 321 332 are also settled

borel extractions of converging sequences in compact sets of borel functions abstract it is well known by a classical result of bourgain fremlin talagrand that if k is a pointwise compact set of borel functions on a polish space then given any cluster point f of a sequence f n n in k one can extract a subsequence f n k k converging to f in the present work we prove that this extraction can be achieved in a borel way this will prove in particular that the notion of analytic subspace of a separable rosenthal compacta is absolute and does not depend on the particular choice of a dense sequence

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates

a small sample model selection criterion based on kullback s symmetric divergence the kullback information criterion kic is a recently developed tool for statistical model selection kic serves as an asymptotically unbiased estimator of a variant within a constant of the kullback symmetric divergence known also as j divergence between the generating model and the fitted candidate model in this paper a bias correction to kic is derived for linear regression models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size for linear regression models the corrected criterion called kicc is an exactly unbiased estimator of the variant of the kullback symmetric divergence assuming that the true model is correctly specified or overfitted furthermore when applied to polynomial regression and autoregressive time series modeling kicc is found to estimate the model order more accurately than any other asymptotically efficient method finally kicc is tested on real data to forecast foreign currency exchange rate the result is very interesting in comparison to classical techniques

conjugate operators that preserve the nonconvergence of bounded martingales we show that the conjugate t of an operator t x y with x and y banach spaces satisfies the following dichotomy either t preserves the nonconvergence of bounded martingales in y or there exists a compact operator k x y such that the kernel n t k fails the radon nikod m property

tukey classification of some ideals on ω and the lattices of weakly compact sets in banach spaces abstract we study the lattice structure of the family of weakly compact subsets of the unit ball b x of a separable banach space x equipped with the inclusion relation this structure is denoted by k b x and also with the parametrized family of almost inclusion relations k l e b x where e 0 this structure is denoted by ak b x tukey equivalence between partially ordered sets and a suitable extension to deal with ak b x are used assuming the axiom of analytic determinacy we prove that separable banach spaces fall into four categories namely k b x is equivalent either to a singleton or to or to the family k q of compact subsets of the rational numbers or to the family c of all finite subsets of the continuum also under the axiom of analytic determinacy a similar classification of ak b x is obtained for separable banach spaces not containing l 1 we prove in zfc that k b x ak b x are equivalent to either 0 k q or c the lattice structure of the family of all weakly null subsequences of an unconditional basis is also studied

on classes of banach spaces admitting small universal spaces we characterize those classes c of separable banach spaces admitting a separable universal space y that is a space y containing up to isomorphism all members of c which is not universal for all separable banach spaces the characterization is a byproduct of the fact proved in the paper that the class nu of non universal separable banach spaces is strongly bounded this settles in the affirmative the main conjecture from argyros and dodos 2007 our approach is based among others on a construction of l spaces due to j bourgain and g pisier as a consequence we show that there exists a family y 1 of separable non universal l spaces which uniformly exhausts all separable banach spaces a number of other natural classes of separable banach spaces are shown to be strongly bounded as well

unconditional families in banach spaces it is shown that for every separable banach space x with non separable dual the space x contains an unconditional family of size x the proof is based on ramsey theory for trees and finite products of perfect sets of reals among its consequences it is proved that every dual banach space has a separable quotient

shellable weakly compact subsets of c 0 1 we show that for every weakly compact subset k of c 0 1 with finite cantor bendixson rank there is a reflexive banach lattice e and an operator t e rightarrow c 0 1 such that k subseteq t b e on the other hand we exhibit an example of a weakly compact set of c 0 1 homeomorphic to omega omega 1 for which such t and e cannot exist this answers a question of m talagrand in the 80 s

operators whose dual has non separable range let x and y be separable banach spaces and t x y be a bounded linear operator we characterize the non separability of t y by means of fixing properties of the operator t