sharp generalizations of the multilinear bohnenblust hille inequality we prove that the multilinear bohnenblust hille inequality is a particular case of a quite general family of optimal inequalities

lipschitz p summing multilinear operators abstract we apply the geometric approach provided by operators to develop a theory of p summability for multilinear operators in this way we introduce the notion of lipschitz p summing multilinear operators and show that it is consistent with a general panorama of generalization namely they satisfy pietsch type domination and factorization theorems and generalizations of the inclusion theorem grothendieck s coincidence theorems the weak dvoretsky rogers theorem and a lindenstrauss pelczynsky theorem we also characterize this new class in tensorial terms by means of a chevet saphar type tensor norm moreover we introduce the notion of dunford pettis multilinear operators with them we characterize when a projective tensor product contains l 1 relations between lipschitz p summing multilinear operators with dunford pettis and hilbert schmidt multilinear operators are given

multiple rademacher means and their applications abstract we evaluate multiple rademacher means for various classes of multilinear operators under the assumption that the range has cotype q these results show that the class of multiple q 2 summing operators plays an important role further we get new extensions of bu s theorem in the multilinear case

on the cohen strongly p summing multilinear operators abstract in this paper we introduce and study a new concept of summability in the category of multilinear operators which is the cohen strongly p summing multilinear operators we prove a natural analog of the pietsch domination theorem and we compare the notion of p dominated multilinear operators with this class by generalizing a theorem of bu cohen

there exist multilinear bohnenblust hille constants cn n 1 with limn cn 1 cn 0 abstract the n linear bohnenblust hille inequality asserts that there is a constant c n 1 such that the l 2 n n 1 norm of u e i 1 e i n i 1 i n 1 n is bounded above by c n times the supremum norm of u for any n linear form u c n c n c and n n the same holds for real scalars we prove what we call fundamental lemma which brings new information on the optimal constants k n n 1 for both real and complex scalars for instance k n 1 k n 0 87 n 0 473 for infinitely many n s for complex scalars we give a formula of surprisingly low growth in which e and the famous euler mascheroni constant appear k n 1 4 1 e 2 1 2 j 1 n 1 j log 2 e 2 1 2 1 n 2 we study the interplay between the kahane salem zygmund and the bohnenblust hille polynomial and multilinear inequalities and provide estimates for bohnenblust hille type inequality constants for any exponent q 2 n n 1

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

strongly p summing multilinear operators abstract we define the concept of strongly p summing multilinear operators and prove that they have properly defined aron berner extensions some properties and examples are shown

coordinatewise multiple summing operators in banach spaces we invent the new notion of coordinatewise multiple summing operators in banach spaces and use it to study various vector valued extensions of the well know bohnenblust hille inequality which originally extended littlewood s 4 3 inequality our results have application on the summability of monomial coefficients of m homogeneous polynomials p l lp as well as for the convergence theory of products of vector valued dirichlet series

a general pietsch domination theorem in this short communication we show that the unified pietsch domination theorem proved in botelho et al 2010 1 remains true even if we remove two of its hypotheses

a tensor norm preserving unconditionality for lp spaces we show that for each n n there is an n tensor norm a in the sense of grothendieck with the surprising property that the tensor product y 1 y n has local unconditional structure for each choice of n arbitrary cp j spaces yj in fact a is the tensor norm associated to the ideal of multiple 1 summing n linear forms on banach spaces

perturbation of resonances in quantum mechanics schrodinger operators on l2 r3 of the form v with potentials v real analytic in are discussed the analytic structure in v and k with k2 the energy variable of the resolvent kernel the eigenvalues and resonances is exhibited and we obtain in particular convergent perturbation expansions for the resonances and the corresponding resonance functions the lower order expansion coefficients are computed explicitly the resonances and the corresponding functions are also computed for a particle moving under the action of n point interactions this gives asymptotic low energy information about schrodinger hamiltonians with short range potentials the perturbation theory of resonances eigenvalues and of the corresponding functions for hamiltonians describing n point interactions perturbed by a potential is also given

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

asymptotic stability of solitary waves we show that the family of solitary waves 1 solitons of the korteweg de vries equation partial t u u partial x u partial x 3 u 0 is asymptotically stable our methods also apply for the solitary waves of a class of generalized korteweg de vries equations partial t u partial x f u partial x 3 u 0 in particular we study the case wheref u up 1 p 1 p 1 2 3 and 3 0 withf c4 the same asymptotic stability result for kdv is also proved for the casep 2 the modified korteweg de vries equation we also prove asymptotic stability for the family of solitary waves for all but a finite number of values ofp between 3 and 4 the solitary waves are known to undergo a transition from stability to instability as the parameterp increases beyond the critical valuep 4 the solution is decomposed into a modulating solitary wave with time varying speedc t and phase t bound state part and an infinite dimensional perturbation radiating part the perturbation is shown to decay exponentially in time in a local sense relative to a frame moving with the solitary wave asp 4 the local decay or radiation rate decreases due to the presence of aresonance pole associated with the linearized evolution equation for solitary wave perturbations

a unified pietsch domination theorem in this paper we prove an abstract version of pietsch s domination theorem which unify a number of known pietsch type domination theorems for classes of mappings that generalize the ideal of absolutely p summing linear operators a final result shows that pietsch type dominations are totally free from algebraic conditions such as linearity multilinearity etc

new upper bounds for the constants in the bohnenblust hille inequality a classical inequality due to bohnenblust and hille states that for every positive integer m there is a constant c m 0 so that sigma n i1 im 1 vertical bar u e i1 e im vertical bar 2m m 1 m 1 2m c where c m m m 1 2m 2 m 1 2 the value of c m was improved to c m 2 m 1 2 by s kaijser and more recently h queffelec and a defant and p sevilla peris remarked that c m 2 root pi m 1 also works the bohnenblust hille inequality also holds for real banach spaces with the constants c m 2 m 1 2 in this note we show that a recent new proof of the bohnenblust hille inequality due to defant popa and schwarting provides in fact quite better estimates for c m for all values of m is an element of n in particular we will also show that for real scalars if m is even with 2 m 24 then c r m 2 1 2 c r m 2 we will mainly work on a paper by defant popa and schwarting giving some remarks about their work and explaining how to numerically improve the previously mentioned constants

p q dominated multilinear operators and lapreste tensor norms abstract we introduce a notion of p q dominated multilinear operators which stems from the geometrical approach provided by operators we prove that p q dominated multilinear operators can be characterized in terms of their behavior on finite sequences and in terms of their relation with a lapreste tensor norm we also prove that they satisfy a generalization of the pietsch s domination theorem and kwapien s factorization theorem also we study the collection d p q of all p q dominated multilinear operators showing that d p q has a maximal ideal demeanor and that the lapreste norm has a finitely generated behavior

conjugacy ofalt5andsl 2 5 subgroups ofe6 c f4 c and a subgroup ofe8 c of typea2e6 we classifyalt5andsl 2 5 subgroups ofe6 c andf4 c up to conjugacy we then use our results to answer conjugacy questions aboutalt5andsl 2 5 subgroups ofe8 c which were not resolved in earlier work

an abstract result on cohen strongly summing operators abstract we present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of cohen strongly summing linear operators our argument is extended to multilinear operators and as a consequence we establish some alternative characterizations for the class of cohen strongly summing multilinear operators

schatten von neumann classes of multilinear forms the authors establish a number of results concerning normed ideals of multilinear forms in banach spaces which extend the theory of trace ideals of operators on hilbert space to such multilinear forms for example it is shown that the dual of the space of compact forms is the space of nuclear forms while the second dual is the space of bounded forms moreover a direct analogue of the schatten p ideals of operators on hilbert space is defined using interpolation techniques and a normal form for compact forms is introduced

improving the closed formula for subpolynomial constants in the multilinear bohnenblust hille inequalities abstract for k r or c the bohnenblust hille inequality asserts that there exists a sequence of scalars c k m m 1 such that i 1 i m 1 n u e i 1 e i m 2 m m 1 m 1 2 m c k m sup z 1 z m d n tu z 1 z m for all m linear forms u k n k n k and every positive integer n where e i i 1 n denotes the canonical basis of k n and d n represents the open unit polydisc in k n very recently 2012 it was shown that there exist constants c k m m 1 with subpolynomial growth satisfying this inequality however these constants were obtained via a complicated recursive formula we improve the best known closed non recursive approximation for these constants

factorization of absolutely continuous polynomials abstract in this paper we study the ideal of dominated p continuous polynomials that extend the nowadays well known ideal of p dominated polynomials to the more general setting of the interpolated ideals of polynomials we give the polynomial version of pietsch s factorization theorem for this new ideal although based on botelho et al in press 16 our factorization theorem requires new techniques inspired in the theory of banach lattices

multichannel nonlinear scattering for nonintegrable equations ii the case of anisotropic potentials and data abstract the nonlinear scattering and stability results of soffer and weinstein comm math phys 1990 are extended to the case of anisotropic potentials and data the range of nonlinearities for which the theory is shown to be valid is also extended considerably

asymptotic expansions in time for solutions of schrodinger type equations let ia i p d v be a dissipative operator in l2 rn where p d is an elliptic differential operator of order m with real constant coefficients and v is a compact operator from the weighted sobolev space hm s rn to h0 p s rn s r for some m 1 let r z be the resolvent of a then an asymptotic expansion of r z as z approaches a critical value of the polynomial p is given the coefficient operators in the expansion are computed explicitly by using the resolvent expansion and the results of m murata 9 an asymptotic expansion of e ita as t is given

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

a new multilinear insight on littlewood s 4 3 inequality abstract we unify littlewood s classical 4 3 inequality a forerunner of grothendieck s inequality together with its m linear extension due to bohnenblust and hille which originally settled bohr s absolute convergence problem for dirichlet series with a scale of inequalties of bennett and carl in l p spaces which are of fundamental importance in the theory of eigenvalue distribution of power compact operators as an application we give estimates for the monomial coefficients of homogeneous l p valued polynomials on c 0

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

abstract extrapolation theorems for absolutely summing nonlinear operators in this paper we prove a general version of the extrapolation theorem for absolutely summing nonlinear operators it is explicitly shown that this result encompasses the previous old and recent linear and nonlinear extrapolation theorems as particular cases one of the steps of the proof provides another nonlinear extrapolation theorem of independent interest

pietsch s factorization theorem for dominated polynomials abstract we prove that like in the linear case there is a canonical prototype of a p dominated homogeneous polynomial through which every p dominated polynomial between banach spaces factors

subgroups of lie type groups containing a unipotent radical abstract in this paper we show that if g is a lie type group and r a proper subgroup of g containing some unipotent radical then r has a nilpotent normal subgroup generated by long root subgroups and r is contained in a proper parabolic subgroup of g we also obtain some consequences of this result

factorization of q p summing polynomials through lorentz spaces abstract we present a vector valued duality between factorable q p summing polynomials and q p summing linear operators on symmetric tensor products of banach spaces several applications are provided first we prove a polynomial characterization of cotype of banach spaces we also give a variant of pisier s factorization through lorentz spaces of factorable q p summing polynomials from c k spaces finally we show a coincidence result for q p concave polynomials

the asymptotic growth of the constants in the bohnenblust hille inequality is optimal the search of sharp estimates for the constants in the bohnenblust hille inequality besides its challenging nature has quite important applications in different fields of mathematics and physics for homogeneous polynomials it was recently shown that the bohnenblust hille inequality for complex scalars is hypercontractive this result interesting by itself has found direct striking applications in the solution of several important problems for multilinear mappings precise information on the asymptotic behavior of the constants of the bohnenblust hille inequality is of particular importance for applications in quantum information theory and multipartite bell inequalities in this paper using elementary tools we prove a quite surprising result the asymptotic growth of the constants in the multilinear bohnenblust hille inequality is optimal besides its intrinsic mathematical interest and potential applications to different areas the mathematical importance of this result also lies in the fact that all previous estimates and related results for the last 80 years such as for instance the multilinear version of the famous grothendieck theorem for absolutely summing operators always present constants c m s growing at an exponential rate of certain power of m

absolutely summing multilinear operators via interpolation abstract we use an interpolative technique from 1 to introduce the notion of multiple n separately summing operators our approach extends and unifies some recent results for instance we recover the best known estimates of the multilinear bohnenblust hille constants due to f bayart d pellegrino and j seoane sepulveda more precisely as a consequence of our main result for 1 t 2 and m 1 we prove that i 1 i m 1 u e i 1 e i m 2 t m 2 m 1 t 2 m 1 t 2 t m j 2 m 2 2 t j t 2 t 2 t j 2 2 2 t 2 j t u for all complex m linear forms u c 0 c 0 c

weighted energy decay for 1d wave equation we obtain a dispersive long time decay in weighted energy norms for solutions to the 1d wave equation with generic potential the decay extends the results obtained by murata for the 1d schrodinger equation

on summability of nonlinear mappings a new approach the main goal of this paper is to characterize arbitrary nonlinear non multilinear mappings f x 1 times cdots times x n rightarrow y between banach spaces that satisfy a quite natural pietsch domination type theorem around a given point a 1 ldots a n in x 1 times cdots times x n as a consequence of our approach a notion of weighted summability arises naturally which may be an interesting topic for further investigation

unconditional basis and gordon lewis constants for spaces of polynomials abstract no infinite dimensional banach space x is known which has the property that for m 2 the banach space of all continuous m homogeneous polynomials on x has an unconditional basis following a program originally initiated by gordon and lewis we study unconditionality in spaces of m homogeneous polynomials and symmetric tensor products of order m in banach spaces we show that for each banach space x which has a dual with an unconditional basis x i the approximable nuclear m homogeneous polynomials on x have an unconditional basis if and only if the monomial basis with respect to x i is unconditional moreover we determine an asymptotically correct estimate for the unconditional basis constant of all m homogeneous polynomials on l n p and use this result to narrow down considerably the list of natural candidates x with the above property

d4 modular forms in this paper we study modular forms on two simply connected groups of type d 4 over q one group g s is a globally split group of type d 4 viewed as the group of isotopies of the split rational octonions the other g c is the isotopy group of the rational nonsplit octonions we study automorphic forms on g s in analogy to the work of gross gan and savin on g 2 namely we study automorphic forms whose component at infinity corresponds to a quaternionic discrete series representation we study automorphic forms on g c using gross s formalism of algebraic modular forms finally we follow work of gan savin gross rallis and others to study an exceptional theta correspondence connecting modular forms on g c and g s this can be thought of as an octonionic generalization of the jacquet langlands correspondence

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

cotype and q 1 summing norm in a banach space we use modern probabilistic methods to gain a better understanding of what it means that a banach space fails to be of cotypeq q 2 in particular we prove that a banach space is of cotypeq if and only if the identity map is q 1 summing in a previous work we had shown that this fails forq 2

freudenthal triple systems in arbitrary characteristic abstract let q v k be the form of degree 4 and h the alternating bilinear form that together give rise to a freudenthal triple system when the characteristic of k is different from 2 and 3 we give a form of degree 4 on a central cover of v over an arbitrary field in arbitrary characteristic and determine the group of similitudes of this group coincides with the intersection of the group of similitudes of q and the isometry group of h when the characteristic is different from 2 and 3 and has the expected structure of a suitable levi subgroup in general we extend known results about the stabilizers of elements of v and orbits of the group of similitudes and show in particular the existence of an exotic set of orbits when char k 2 and k is not perfect

bohr s strip for vector valued dirichlet series bohr showed that the width of the strip in the complex plane on which a given dirichlet series sum a n n s s in mathbb c converges uniformly but not absolutely is at most 1 2 and bohnenblust hille that this bound in general is optimal we prove that for a given infinite dimensional banach space y the width of bohr s strip for a dirichlet series with coefficients an in y is bounded by 1 1 cot y where cot y denotes the optimal cotype of y this estimate even turns out to be optimal and hence leads to a new characterization of cotype in terms of vector valued dirichlet series

sharp coincidences for absolutely summing multilinear operators abstract in this paper we prove the optimality of a family of known coincidence theorems for absolutely summing multilinear operators we connect our results with the theory of multiple summing multilinear operators and prove the sharpness of similar results obtained via the complex interpolation method

linear preservers and representations with a 1 dimensional ring of invariants we determine the group of linear transformations on a vector space v that preserve a polynomial function f on v for several interesting pairs v f using the theory of semisimple algebraic groups in an 1897 paper fro97 frobenius proved that every linear transformation of the n by n real matrices that preserves the determinant is of the form x 7 axb or x 7 ax t b for some a b gln r such that det ab 1 this is the basic example of a linear preserver problem lpp one is given a finite dimensional vector space v over a field k and a polynomial function f v k and one wants to determine the linear transformations of v that preserve f since frobenius many such prob lems have been solved see for example the surveys lp01 pll 92 lt92 and mar62 we develop here a general method that solves several new problems see examples 3 14 and 3 15 and corollaries 7 10 8 3 8 7 8 5 8 8 and 8 11 our method is to introduce an auxiliary group g gl v that is semisimple and such that v is an irreducible representation or weyl module of g in section 2 we determine the normalizer ngl v g of g in gl v we prove in theorem 3 2 that this subgroup equals the stabilizer of a closed g orbit o in the projective space p v i e stabgl v o ngl v g using this result in sections 7 and 8 we solve two families of lpps by reducing the problems in each family to determining this stabilizer these two families consist of representations v with a 1 dimensional ring of g invariant functions generated by f and are examples of prehomogenous vector spaces of parabolic type the two families correspond to the cases where the unipotent radical u of the parabolic subgroup is abelian i e u u 0 or u u is 1 dimensional respectively and we use the general results on representations in these families from rrs92 roh93 and hel12 besides obtaining new results we also recover many known solutions to linear preserver problems the generality of our method is in contrast to many of the proofs in the literature which typically are highly dependent on the particular choice of v and f the arguments in pd95 and gur97 are notable exceptions further we require only very weak assumptions about the field k at most we require that the characteristic is 6 2 3 and determine the preserver precisely and not just its identity component or lie algebra

on the bohnenblust hille inequality and a variant of littlewoodʼs 4 3 inequality the search for sharp constants for inequalities of the type littlewood s 4 3 and bohnenblust hille has lately shown unexpected applications in many fields such as analytic number theory quantum information theory or in results on n dimensional bohr radii recent estimates obtained for the multilinear bohnenblust hille inequality for real scalars have been used as a crucial tool by a montanaro in order to solve problems in quantum xor games here among other results we obtain new upper bounds for the bohnenblust hille constants for complex scalars for bilinear forms we provide optimal constants of variants of littlewood s 4 3 inequality for real scalars when the exponent 4 3 is replaced by any r 4 3 we also prove that the optimal constants in real case are always strictly greater than those from the complex case

volume estimates in spaces of homogeneous polynomials given m we derive upper and lower estimates for the volume of the unit ball of the banach space mathcal p m e n all m homogeneous polynomials defined on the nth section e n of a symmetric banach sequence space e with constants depending on m only we apply this result to obtain asymptotically correct orders of various important invariants of mathcal p m e n from local banach space theory as e g volume ratios cotype and type 2 constants projection constants or banach mazur distances

weighted decay estimates for the wave equation abstract in this work we study weighted sobolev spaces in r n generated by the lie algebra of vector fields 1 x 2 1 2 x j j 1 n interpolation properties and sobolev embeddings are obtained on the basis of a suitable localization in r n as an application we derive weighted l q estimates for the solution of the homogeneous wave equation for the inhomogeneous wave equation we generalize the weighted strichartz estimate established by v georgiev 1997 amer j math 119 1291 1319 and establish global existence results for the supercritical semilinear wave equation with non compact small initial data in these weighted sobolev spaces

polynomial characterization of l spaces it is shown that given an index m a banach space e is an l space if and only if every 1 dominated m homogeneous polynomial on e is integral this extends a result for linear operators due to stegall and retherford

some non split extensions of the orthogonal group ω 7 3 abstract we will give an explicit construction of the non split extension 3 7 7 3 2 which is a maximal subgroup of fischer s largest 3 transposition group f 24 in the proof of non splitness we use some moufang loop of order 81 by using this loop we can also construct another non split extension 3 7 3 2

the bohnenblust hille inequality for homogeneous polynomials is hypercontractive the bohnenblust hille inequality says that the 2m m 1 norm of the coefcients of an m homogeneous polynomial p on c n is bounded by kpk1 times a constant independent of n wherekk 1 denotes the supremum norm on the polydisc d n the main result of this paper is that this inequality is hypercontractive i e the constant can be taken to be c m for some c 1 combining this improved version of the bohnenblust hille inequality with other results we obtain the following the bohr radius for the polydisc d n behaves asymptotically as p logn n modulo a factor bounded away from 0 and innity

resonances radiation damping and instabilitym in hamiltonian nonlinear wave equations we consider a class of nonlinear klein gordon equations which are hamiltonian and are perturbations of linear dispersive equations the unperturbed dynamical system has a bound state a spatially localized and time periodic solution we show that for ge neric nonlinear hamiltonian perturbations all small amplitude so lutions decay to zero as time tends to infinity at an anomalously slow rate in particular spatially localized and time periodic solutions of the linear problem are destroyed by generic nonlinear hamiltonian perturbations via slow radiation of energy to infinity these solutions can therefore be thought of as metastable states the main mecha nism is a nonlinear resonant interaction of bound states eigenfunc tions and radiation continuous spectral modes leading to energy transfer from the discrete to continuum modes this is in contrast to the kam theory in which appropriate nonresonance conditions im ply the persistence of invariant tori a hypothesis ensuring that such a resonance takes place is a nonlinear analogue of the fermi golden rule arising in the theory of resonances in quantum mechanics the techniques used involve i a time dependent method developed by the authors for the treatment of the quantum resonance problem and perturbations of embedded eigenvalues ii a generalization of the hamiltonian normal form appropriate for infinite dimensional dis persive systems and iii ideas from scattering theory the arguments are quite general and we expect them to apply to a large class of

convergence of dirichlet polynomials in banach spaces both authors were supported by the mec project mtm2008 03211 the second author was partially supported by grants pr2007 0384 mec and upv paid 00 07

multilinear variants of maurey and pietsch theorems and applications we prove composition results for multilinear operators and multilinear variants of maurey and pietsch theorems both for multiple p summing p dominated and p summing multilinear operators

reverse inclusions for multiple summing operators abstract multiple summing operators have been proven to be useful in several areas of analysis and mathematical physics in this paper we prove reverse inclusions for this class of operators completing the work already initiated in d perez garcia the inclusion theorem for multiple summing operators studia math 165 3 2004 275 290

on cohen almost summing multilinear operators abstract we show that all cohen strongly p summing multilinear operators and polynomials on banach spaces are cohen almost summing if the range space is a hilbert space then all cohen strongly p summing multilinear operators and polynomials are strongly q summing 1 p q moreover if both domain and range spaces are hilbert spaces then all hilbert schmidt multilinear operators are cohen strongly 2 summing

on bounded multilinear forms on a class of lp spaces abstract in this paper we generalize an old result of littlewood and hardy about bilinear forms defined in a class of sequence spaces historically littlewood quart j math 1 1930 first proved a result on bilinear forms on bounded sequences and this result was then generalized by hardy and littlewood in a joint paper quart j math 5 1934 to bilinear forms on a class of lp spaces later davie and kaijser proved littlewood s results for multilinear forms in this paper theorems a and b generalize the results to multilinear forms on lp spaces all the results are stated at the end of section 1 theorems a and b are proved respectively in sections 2 and 3

spaces of σ p nuclear linear and multilinear operators on banach spaces and their duals abstract the theory of summing and nuclear linear operators on banach spaces was developed by pietsch 20 chapter 23 extending the linear case to the range p 1 and generalizing all cases to the multilinear setting in this paper we introduce the concept of p nuclear linear and multilinear operators in order to develop the duality theory for the spaces of such operators we introduce the concept of quasi p summing linear multilinear operators and prove pietsch type domination theorems for such operators the main result of the paper shows that under usual conditions linear functionals on the space of p nuclear n linear operators are represented via the borel transform by quasi p summing n linear operators as far as we know this result is new even in the linear case n 1

on the growth of the optimal constants of the multilinear bohnenblust hille inequality let kn n 1 be the optimal constants satisfying the multilinear real or complex bohnenblust hille inequality the exact values of the constants kn are still waiting to be discovered since eighty years ago with the publication of bohnenblust and hille paper in the annals of mathematics recently it was proved that kn n 1 has a subpolynomial growth moreover it is now known that if there is an l such that limn kn kn 1 l then l 0 in this note we show that if there is an l 0 such that limn k2nkn l then l 1 d with d e12 12 for real scalars and d e1 12 2 for complex scalars here is the famous euler mascheroni constant we show that this result generalizes the former

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