bohr inequalities for free holomorphic functions on polyballs abstract multivariable operator theory is used to provide bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball b n n n 1 n k n k which is a noncommutative analogue of the scalar polyball c n 1 1 c n k 1 the bohr radius k m h b n resp k h b n associated with the multi homogeneous resp homogeneous power series expansions of the free holomorphic functions are the main objects of study in this paper we extend a theorem of bombieri and bourgain for the disc d z c z 1 to the polyball and obtain the estimations 1 3 k k m h b n 2 log k k if k 1 extending boas khavinson result for the scalar polydisc d k with respect to the homogeneous power series expansion we prove that k h b n 1 3 extending the classical result and obtain analogues of caratheodory fejer and egervary szasz inequalities for free holomorphic functions with operator coefficients and positive real parts on the polyball these results are used to provide multivariable analogues of landau s inequality and bohr s inequality when the norm is replaced by the numerical radius of an operator when specialized to the regular polydisc d k which corresponds to the case n 1 n k 1 we obtain new results concerning bohr landau fejer and harnack inequalities for operator valued holomorphic functions and k pluriharmonic functions on the scalar polydisc d k the results of the paper can be used to obtain bohr type inequalities for the noncommutative ball algebra a n the hardy algebra f n and the c algebra c s generated by the universal model s of the polyball b n

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

relative oscillation non oscillation criteria for perturbed periodic dirac systems under minimal hypotheses sufficient criteria for a perturbed dirac system to be relatively oscillatory or non oscillatory at with respect to a reference equation with periodic coefficients are proved my means of an asymptotic analysis of generalized prufer angles as illustrated by an example they help decide whether the number of eigenvalues in gaps of the essential spectrum is finite or infinite the critical perturbations naturally occur in the partial wave analysis of spherically symmetric dirac operators

banach spaces of general dirichlet series abstract we study when the spaces of general dirichlet series bounded on a half plane are banach spaces and show that some of those classes are isometrically isomorphic between themselves in a precise way let n be a strictly increasing sequence of positive real numbers such that lim n n we denote by h n the complex normed space of all dirichlet series d s n b n n s which are convergent and bounded on the half plane re s 0 endowed with the norm d sup re s 0 d s if there exists q 0 such that inf n n 1 q n q 0 then h n is a banach space further if there exists a strictly increasing sequence r n of positive numbers such that the sequence log r n is q linearly independent n r for n p and n is the increasing rearrangement of the sequence n then h n is isometrically isomorphic to h b c 0 with this condition we explain more explicitly the optimal cases of the difference among the abscissas c b u and a

generalization of a theorem of bohr for bases in spaces of holomorphic functions of several complex variables abstract in the first part we generalize the classical result of bohr by proving that an analogous phenomenon occurs whenever d is an open domain in c m or more generally a complex manifold and n n 0 is a basis in the space of holomorphic functions h d such that 0 1 and n z0 0 n 1 for some z0 d namely then there exists a neighborhood u of the point z0 such that whenever a holomorphic function on d has modulus less than 1 the sum of the suprema in u of the moduli of the terms of its expansion is less than 1 too in the second part we consider some natural hilbert spaces of analytic functions and derive necessary and sufficient conditions for the occurrence of bohr s phenomenon in this setting

a subexponential vector valued bohnenblust hille type inequality abstract bayart pellegrino and seoane recently proved that the polynomial bohnenblust hille inequality for complex scalars is subexponential we show that a vector valued polynomial bohnenblust hille inequality on complex banach lattices is also subexponential for some special cases our main result recovers the best known constants of the classical polynomial inequality provided in 4

on the essential spectrum of schrodinger operators with spherically symmetric potentials on determine le spectre essentiel des operateurs de schrodinger avec un potentiel a symetrie spherique v x q x

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 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

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

holomorphic semi groups and the geometry of banach spaces according to a fundamental theorem of dvoretzky cf 24 25 any infinite dimensional banach space x contains for each integer n and each e 0 a subspace xn which is 1 e isomorphic to 12n in the classical banach spaces lp and 1p with 1 p x it is well known that this result can be improved these spaces contain uniformly complemented ln 7 s this means that we can find subspaces xn as above with the additional property that there exist projections p x xn such that supn 11 pn 11 cx moreover it is also well known that this property no longer holds for 11 or lo this motivated the question cf 13 to determine which infinite dimensional banach spaces contain uniformly complemented 1 n s we will prove below that all uniformly convex spaces have this property moreover we will show that a banach space x verifies this property locally see definition 2 10 for more precision if and only if x does not contain l n s uniformly progressively the work of previous authors cf 14 12 and particularly 5 has reduced such so called geometric questions to a purely analytic problem consisting of verifying in x a certain inequality referred to as k convexity in this paper we connect this inequality with the holomorphy of a certain semi group of operators on lp x and we show how this leads to the results already mentioned

sharp bohr type inequality abstract this article is devoted to the sharp improvement of the classical bohr inequality for bounded analytic functions defined on the unit disk we also prove two other sharp versions of the bohr inequality by replacing the constant term by the absolute of the function and the square of the absolute of the function respectively

random unconditional convergence of vector valued dirichlet series abstract we study random unconditionality of dirichlet series in vector valued hardy spaces h p x it is shown that a banach space x has type 2 respectively cotype 2 if and only if for every choice x n n x it follows that x n n s n is random unconditionally convergent respectively divergent in h 2 x the analogous question on h p x spaces for p 2 is also explored we also provide explicit examples exhibiting the differences between the unconditionality of x n n s n in h p x and that of x n z n n in h p x

type and cotype in vector valued nakano sequence spaces abstract given a sequence of banach spaces xn n and a sequence of real numbers pn n in 1 the vector valued nakano sequence spaces l pn xn consist of elements xn n in nxn for which there is a constant 0 such that n xn pn

asymptotics of the bohr radius for polynomials of fixed degree we obtain a characterization and conjecture asymptotics of the bohr radius for the class of complex polynomials in one variable our work is based on the notion of bound preserving operators

vector valued hausdorff young inequality on compact groups the main purpose of this paper is to study the validity of the hausdorff young inequality for vector valued functions defined on a non commutative compact group as we explain in the introduction the natural context for this research is that of operator spaces this leads us to formulate a whole new theory of fourier type and cotype for the category of operator spaces the present paper is the first step in this program where the basic theory is presented the main examples are analyzed and some important questions are posed

algebraic cycles from a computational point of view the hodge conjecture implies decidability of the question whether a given topological cycle on a smooth projective variety over the field of algebraic complex numbers can be represented by an algebraic cycle we discuss some details concerning this observation and then propose that it suggests going on to actually implement an algorithmic search for algebraic representatives of classes which are known to be hodge classes

fundamental group and contractible closed geodesics we prove the existence of a nonempty class of finitely presented groups with the following property if the fundamental group of a compact riemannian manifold m belongs to this class then there exists a constant c m 1 such that for any sufficiently large x the number of contractible closed geodesics on m of length not exceeding x is greater than c m x in order to prove this result we give a lower bound for the number of contractible closed geodesics of length x on a compact riemannian manifold m in terms of the resource bounded kolmogorov complexity of the word problem for 1 m thus answering a question posed by gromov 1996 john wiley sons inc

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

isometries between spaces of multiple dirichlet series abstract in this paper we study spaces of multiple dirichlet series and their properties we set the ground of the theory of multiple dirichlet series and define the spaces h c k k n of convergent and bounded multiple dirichlet series on c k we give a representation for these banach spaces and prove that they are all isometrically isomorphic independently of the dimension the analogous result for a c k k n which are the spaces of multiple dirichlet series that are convergent on c k and define uniformly continuous functions is obtained

multipliers of dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables let mathscr h infty be the set of all ordinary dirichlet series d sum n a n n s representing bounded holomorphic functions on the right half plane a completely multiplicative sequence b n of complex numbers is said to be an ell 1 multiplier for mathscr h infty whenever sum n a n b n infty for every d in mathscr h infty we study the problem of describing such sequences b n in terms of the asymptotic decay of the subsequence b p j where p j denotes the jth prime number given a completely multiplicative sequence b b n we prove among other results b is an ell 1 multiplier for mathscr h infty provided b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 1 and conversely if b is an ell 1 multiplier for mathscr h infty then b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 le 1 here b stands for the decreasing rearrangement of b following an ingenious idea of harald bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk mathbb d infty the open unit ball of ell infty for which every bounded and holomorphic function f on mathbb d infty has an absolutely convergent monomial series expansion sum alpha frac partial alpha f 0 alpha z alpha moreover we study analogous problems in hardy spaces of dirichlet series and hardy spaces of functions on the infinite dimensional polytorus mathbb t infty

atomic decompositions for tensor products and polynomial spaces abstract we study the existence of atomic decompositions for tensor products of banach spaces and spaces of homogeneous polynomials if a banach space x admits an atomic decomposition of a certain kind we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product s n x for any symmetric tensor norm in addition the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on x

new families of nonreflexive banach spaces with the fixed point property abstract in this paper we define the concept of sequentially separating norm and we relate it to the fulfillment of the fixed point property for nonexpansive mappings we develop a technique to construct families of nonreflexive banach spaces with the fixed point property different examples will be exhibited we also study the geometry of the banach spaces that can be renormed with a sequentially separating norm

geometry of the space of triangulations of a compact manifold in this paper we study the spacetm of triangulations of an arbitrary compact manifoldm of dimension greater than or equal to four this space can be endowed with the metric defined as the minimal number of bistellar operations required to transform one of two considered triangulations into the other recently this space became and object of study in quantum gravity because it can be regarded as a toy discrete model of the space of riemannian structures onm

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

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

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

exceptional coupling constants for the coulomb dirac operator with anomalous magnetic moment it was recently shown that the point spectrum of the separated coulomb dirac operator h0 k is the limit of the point spectrum of the dirac operator with anomalous magnetic moment ha k as the anomaly parameter tends to 0 this spectral stability holds for all coulomb coupling constants c for which h0 k has a distinguished self adjoint extension if the angular momentum quantum number k is negative but for positive k there are certain exceptional values for c here we obtain an explicit formula for these exceptional values in particular it implies spectral stability for the three dimensional coulomb dirac operator if c 1 covering all physically relevant cases

holomorphic mappings on we describe the holomorphic mappings of bounded type and the arbitrary holomorphic mappings from the complex banach space 11 into a complex banach space x it is shown that these mappings have monomial expansions and the growth of the norms of the coefficients is characterized in each case this characterization is used to give new descriptions of the compact open topology and the nachbin ported topology on the space a 11 x of holomorphic mappings and to prove a lifting property for holomorphic mappings on 11 we also show that the monomials form an equicontinuous unconditional schauder basis for the space 11 so of holomorphic functions on 11 with the topology of uniform convergence on compact sets

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

reinhardt domains of holomorphy in banach spaces abstract it is known that in c 0 the holomorphic functions representable by multiple power series the series of monomials are those of nuclear type in this article we show that in a banach space with unconditional schauder basis every domain of existence is the domain of existence of a holomorphic function representable by a multiple power series and in fact the domain of convergence of such a series

critical coupling constants and eigenvalue asymptotics of perturbed periodic sturm liouville operators perturbations of asymptotic decay c r 2 arise in the partial wave analysis of rotationally symmetric partial differential operators we show that for each end point 0 of the spectral bands of a perturbed periodic sturm liouville operator there is a critical coupling constant c crit such that eigenvalues in the spectral gap accumulate at 0 if and only if c c crit 1 the oscillation theoretic method used in the proof also yields the asymptotic distribution of the eigenvalues near 0

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

polynomials on riesz spaces abstract in this paper we investigate polynomial mappings on riesz spaces we give a characterization of positivity of homogeneous polynomials in terms of forward differences finally we prove hahn banach type extension theorems for positive and regular polynomial mappings

eigenvalues in gaps of perturbed periodic dirac operators numerical evidence this paper presents a method for the numerical investigation of the distribution of the eigenvalues introduced into a spectral gap of a periodic dirac system by a perturbation of the type of the angular momentum term a number of examples illustrate the effectiveness of the method and show the remarkable accuracy of the strong coupling asymptotic formula even for small values of the perturbation coupling constant furthermore the results shed some light on the spectrum in the exceptional gap of radially periodic three dimensional dirac operators

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

lower bounds for the complex polynomial hardy littlewood inequality abstract the hardy littlewood inequality for complex homogeneous polynomials asserts that given positive integers m 2 and n 1 if p is a complex homogeneous polynomial of degree m on l p n with m p given by p x 1 x n m a x then there exists a constant c c m p pol 1 which does not depend on n such that m a 1 c c m p pol sup z b l p n p z with p p m if m p 2 m and 2 m p m p p 2 m if 2 m p in this short note we provide nontrivial lower bounds for the constants c c m p pol for instance we prove that for m 2 and m p c c m p pol 2 m p for m even and c c m p pol 2 m 1 p for m odd estimates for the case p this is the particular case of the complex polynomial bohnenblust hille inequality were recently obtained by d nunez alarcon in 2013

bilinear interpolation theorems and applications abstract interpolation of bilinear operators is studied the celebrated littlewood mixed norm inequality is used to prove interpolation theorems for bilinear operators defined on couples of c 0 weighted sequence spaces generated by parameters of quasi concave functions it is shown that these results can be lifted to a wider class of abstract methods of interpolation the abstract results are used to prove bilinear interpolation theorems to the setting of calderon lozanovskii spaces as an application the boundedness of the bilinear hilbert transform between orlicz spaces including zygmund classes is proved

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

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

bohr radii of vector valued holomorphic functions abstract motivated by the scalar case we study bohr radii of the n dimensional polydisc d n for holomorphic functions defined on d n with values in banach spaces

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

abscissas of weak convergence of vector valued dirichlet series abstract the abscissas of convergence uniform convergence and absolute convergence of vector valued dirichlet series with respect to the original topology and with respect to the weak topology x x of a locally convex space x in particular of a banach space x are compared the relation of their coincidence with geometric or topological properties of the underlying space x is investigated cotype in the context of banach spaces and nuclearity and certain topological invariants for frechet spaces play a relevant role

type and cotype of musielak orlicz sequence spaces let n be a musielak orlicz function and l the musielak orlicz sequence space generated by it is shown that satisfies condition qiff is equivalent to aq concave function n it is also proved thatl is of cotypeq typep if and only if satisfies condition q 2and pconditions respectively as applications we obtain characterization of the type and cotype of various sequence spaces nakano weighted orlicz and orlicz sequence spaces furthermore a relation betweenq concavity p convexity lowerq estimate upperp estimate and cotype type of l is given

some polynomial versions of cotype and applications abstract we introduce non linear versions of the classical cotype of banach spaces we show that spaces with l u st and cotype and spaces having fourier cotype enjoy our non linear cotype we apply these concepts to get results on convergence of vector valued power series in infinite many variables and on l 1 multipliers of vector valued dirichlet series finally we introduce cotype with respect to indexing sets an idea that includes our previous definitions