doubly optimal homogeneous trace sobolev inequality in a solid torus abstract in this paper using techniques that exploit the symmetry presented by the solid torus we study the problem of determining both the best constants for the doubly homogeneous trace sobolev inequality which in the general case studied by maggi and villani in 16

strong primeness of hermitian jordan systems this paper establishes the strong primeness of all jordan systemsjof hermitian type trapped between ample hermitian elements of a prime associative systemrand its martindale system of symmetric quotientsq r h0 r j h q r this completes the converse of zelmanov s classification of strongly prime jordan systems providing if as well as only if classifications of strongly prime and primitive jordan systems

subsets of some families of real functions and their algebrability abstract we consider the following families of real valued functions darboux d quasi continuous q and wi tkowski functions s the aim of this paper is to study the level of algebrability for various intersections of families d q and s and their complements

local and subquotient inheritance of simplicity in jordan systems abstract in this paper we prove that the local algebras of a simple jordan pair are simple jordan pairs all of which local algebras are simple are also studied showing that they have a nonzero simple heart which is described in terms of powers of the original pair similar results are given for jordan triple systems and algebras finally we characterize the inner ideals of a simple pair which determine simple subquotients answering the question posed by o loos and e neher 1994 j algebra166 255 295

best constants in sobolev trace inequalities abstract in this paper we establish the best constant for a sobolev trace inequality on compact riemannian manifolds with boundary more specifically let 1 1 k n p inf u l p r n u l p r n 0 r n u p r n u p p p where p p n 1 n p we prove that for any compact n dimensional riemannian manifold with boundary m g for any e 0 there exists ae 0 such that u l p m p k n p e g u l p m p a e u l p m p for all u h1 p m

nonseparable spaceability and strong algebrability of sets of continuous singular functions abstract let cbv denote the banach algebra of all continuous real valued functions of bounded variation defined in 0 1 we show that the set of strongly singular functions in cbv is nonseparably spaceable we also prove that certain families of singular functions constitute strongly c algebrable sets the argument is based on a criterion of strong c algebrability using compositions with exponential like functions

moduleability algebraic structures and nonlinear properties we show that some pathological phenomena occur more often than one could expect existing large algebraic structures infinite dimensional vector spaces algebras positive cones or infinitely generated modules enjoying certain special properties in particular we construct infinite dimensional vector spaces of non integrable measurable functions completing some recent results shown in garcia pacheco et al 2009 13 garcia pacheco and seoane sepulveda 2006 15 munoz fernandez et al 2008 20 we prove as well the existence of dense and not barrelled spaces of sequences every non zero element of which has a finite number of zero coordinates giving partial answers to a problem originally posed by r m aron and v i gurariy in 2003

spaceability of the set of continuous injections from blp into lp with nowhere continuous inverses abstract let p 1 we show that in the banach space of all bounded continuous mappings from b l p the open unit ball in l p into l p the subset consisting of all injections with nowhere continuous inverses is isometrically l p spaceable i e it contains an isometric copy of l p the proof uses some ideas of creswell s example

strong c algebrability of strong sierpinski zygmund smooth nowhere analytic and other sets of functions abstract we present a useful technique of proving strong c algebrability as an outcome we obtain the strong c algebrability of the following sets of functions strong sierpinski zygmund nowhere holder bruckner garg nowhere monotone differentiable a certain baire class smooth and nowhere analytic functions

lineability criteria with applications lineability is a property enjoyed by some subsets within a vector space x a subset a of x is called lineable whenever a contains except for zero an infinite dimensional vector subspace if additionally x is endowed with richer structures then the more stringent notions of dense lineability maximal dense lineability and spaceability arise naturally in this paper several lineability criteria are provided and applied to specific topological vector spaces mainly function spaces sometimes such criteria furnish unified proofs of a number of scattered results in the related literature families of strict order integrable functions hypercyclic vectors non extendable holomorphic mappings riemann non lebesgue integrable functions sequences not satisfying the lebesgue dominated convergence theorem nowhere analytic functions bounded variation functions entire functions with fast growth and peano curves among others are analyzed from the point of view of lineability

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

global existence for a bulk surface model for active transport induced polarisation in biological cells abstract we consider a coupled bulk surface model for advection and diffusion of interacting chemical species in biological cells specifically we consider a signalling protein that can exist in both a cytosolic and a membrane bound state along with a variable that gives a coarse grained description of the cytoskeleton the main focus of our work is on the well posedness of the model whereby the coupling at the boundary is the main source of analytical difficulty a priori l p estimates together with classical schauder theory deliver global existence of classical solutions for small data on bounded lipschitz domains for two physically reasonable regularised versions of the boundary coupling we are able to prove global existence of solutions for arbitrary data in addition we prove the existence of a family of steady state solutions of the main model which are parametrised by the total mass of the membrane bound signal molecule

spaceability in banach and quasi banach sequence spaces abstract let x be a banach space we prove that for a large class of banach or quasi banach spaces e of x valued sequences the sets e q l q x where is any subset of 0 and e c 0 x contain closed infinite dimensional subspaces of e if non empty of course this result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm attaining linear operators

a note on latticeability and algebrability abstract suppose a is a subset of a banach lattice banach algebra x we look for large sublattices resp subalgebras of a if x is a banach lattice we prove 1 if y is a closed subspace of x of codimension at least n then x y 0 contains a sublattice of dimension n 2 if y is a closed infinite codimensional ideal in x then x y 0 contains a closed infinite dimensional sublattice 3 if the order in x is induced by a 1 unconditional basis and y is a closed infinite codimensional subspace of x then x y 0 contains a closed infinite dimensional ideal further we show that 4 l p q p l q 0 contains a sublattice which is dense in l p and that 5 the sets l 1 t p 1 l p t 0 and s p s p 0 contain a dense subalgebra with a continuum of free generators here s p denotes the schatten p space

analysis of a nonlocal model for spontaneous cell polarization in this work we investigate the dynamics of a nonlocal model describing spontaneous cell polarization it consists of a drift diffusion equation set in the half space with the coupling involving the trace value on the boundary we characterize the following behaviors in the one dimensional case solutions are global if the mass is below the critical mass and they blow up in finite time above the critical mass the higher dimensional case is also discussed the results are reminiscent of the classical keller segel system but critical spaces are different l n instead of l n 2 due to the coupling on the boundary in addition in the one dimensional case we prove quantitative convergence results using relative entropy techniques this work is complemented with a more realistic model that takes into account dynamical exchange of molecular content at the boundary in the one dimensional case we prove that blow up is prevented furthermore density converges toward a nontrivial stationary configuration

additivity and lineability in vector spaces abstract gamez merino munoz fernandez and seoane sepulveda proved that if additivity a f c then f is a f lineable where f r r they asked if a f c can be weakened we answer this question in negative moreover we introduce and study the notions of homogeneous lineability number and lineability number of subsets of linear spaces

imbedding jordan systems in primitive systems we show that special jordan systems j which are free of torsion over a scalar ring imbed in primitive hence strongly prime jordan systems j j heart j with simple primitive heart we show examples of exceptional jordan systems which cannot be imbedded in a nondegenerate system

local pi theory of jordan systems ii abstract in this paper we study jordan systems having nonzero local algebras that satisfy a polynomial identity we prove that in nondegenerate jordan systems the set of elements at which the local algebra is pi is an ideal and that if it is nonzero it coincides with the socle when the system is primitive

linear subsets of nonlinear sets in topological vector spaces for the last decade there has been a generalized trend in mathematics on the search for large algebraic structures linear spaces closed subspaces or infinitely generated algebras composed of mathematical objects enjoying certain special properties this trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis operator theory summability theory polynomials in banach spaces hypercyclicity and chaos and general functional analysis this expository paper is devoted to providing an account on the advances and on the state of the art of this trend nowadays known as lineability and spaceability

asymptotics of best sobolev constants on thin manifolds abstract we study the asymptotic behaviour of best sobolev constants on a compact manifold with boundary that we contract in k directions or to a point we find in the limit best sobolev constants for weighted sobolev spaces of the limit manifold

the jordan algebras of a lie algebra abstract we attach a jordan algebra l x to any ad nilpotent element x of index of nilpotence at most 3 in a lie algebra l this jordan algebra has a behavior similar to that of the local algebra of a jordan system at an element thus l x inherits nice properties from l and keeps relevant information about the element x

the best sobolev trace constant in a domain with oscillating boundary abstract in this paper we study homogenization problems for the best constant for the sobolev trace embedding w 1 p l q in a bounded smooth domain when the boundary is perturbed by adding an oscillation we find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary for sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations

on lineability of sets of continuous functions we study the existence of vector spaces of dimension at least two of continuous functions on subsets of r every non zero element of which admits one and only one absolute maximum

primitive jordan pairs and triple systems abstract in this paper we give a characterization of primitivity of jordan pairs and triple systems in terms of their local algebras as a consequence of that local characterization we extend to jordan pairs and triple systems most of the known results about primitive jordan algebras in particular we describe primitive jordan pairs and triple systems over an arbitrary ring of scalars in the sense of the structure of primitive quadratic jordan algebras by j a anquela t cortes and f montaner 1995 j algebra172 530 553 5 1

herstein s theorems and simplicity of hermitian jordan systems abstract in this paper we extend herstein s first construction relating associative and jordan ideals to pairs and triple systems as a consequence we show that an associative pair or triple system is simple if and only if its jordan symmetrization is simple we also generalize herstein s second construction to ample subsystems of associative algebras pairs and triple systems which provides information on their simplicity when the associative structure is simple

the structure of primitive quadratic jordan algebras in this paper we give a complete description of primitive quadratic jordan algebras following the classification of strongly prime quadratic jordan algebras k mccrimmon and e i zel manov adv math 69 no 2 1988 133 222 the proof is based in two results of independent interest we show that every p i primitive jordan algebra is simple and unital with nonzero socle and prove that associative tight tight envelopes of special primitive jordan algebras are also primitive primitive as a consequence of the latter fact we see that an associative algebra a is one sided primitive if and only if a is primitive and an associative algebra a with involution is primitive if and only if an ample subspace h 0 a is primitive

goldie theory for jordan algebras it is shown that zelmanov s version of goldie s conditions still characterizes quadratic jordan algebras having an artinian algebra of quotients which is nondegenerate at the same time jordan versions of the main notions of the associative theory such as those of the uniform ideal uniform element singular ideal and uniform dimension are studied moreover it is proved that the nondegenerate unital jordan algebras of finite capacity are precisely the algebras of quotients of nondegenerate jordan algebras having the property that an inner ideal is essential if and only if it contains an injective element 2002 elsevier science usa

spaceability of strict order integrability abstract in this paper sharp conditions on a measure space are provided in order that the subset of functions in the corresponding lebesgue space l p which are in no other l q contains except for zero an infinite dimensional closed subspace this completes earlier work of several authors the main result is derived from a new general criterion for spaceability on function spaces a further application to spaceability of the class of non absolutely continuous functions is supplied

lineability in subsets of measure and function spaces we show among other results that if lambda denotes the lebesgue measure on the borel sets in 0 1 and x is an infinite dimensional banach space then the set of measures whose range is neither closed nor convex is lineable in ca lambda x we also show that in certain situations we have lineability of the set of x valued and non sigma finite measures with relatively compact range the lineability of sets of the type l p i l q i is studied and some open questions are proposed some classical techniques together with the converse of the lyapunov convexity theorem are used

primitivity in jordan systems is ubiquitous abstract the main result of the paper asserts that if a jordan pair v v v is primitive at some 0 b v then it is primitive at any 0 b v also if a jordan triple system t is primitive at some 0 b t then it is primitive at any 0 b t as a tool similar results concerning one sided primitivity and primitivity of associative pairs and triple systems are established equivalences between our definitions of primitivity and some other appearing in the literature are also obtained as a consequence

improving l2 estimates to harnack inequalities we consider operators of the form l l v where l is an elliptic operator and v is a singular potential defined on a smooth bounded domainir n with dirichlet boundary conditions we allow the boundary of to be made of various pieces of different codimension we assume that l has a generalized first eigenfunction of which we know two sided estimates under these assumptions we prove optimal sobolev inequalities for the operator l we show that it generates an intrinsic ultracontractive semigroup and finally we derive a parabolic harnack inequality up to the boundary as well as sharp heat kernel estimates

large structures in certain subsets of orlicz spaces abstract assume that and n n 1 are young functions in this paper we prove that under sharp conditions on a measure space and the young functions and n s the subset of functions in the corresponding orlicz space l which are not in l n for all n n admits various large linear structures

the best sobolev trace constant as limit of the usual sobolev constant for small strips near the boundary in this paper we prove that the best constant in the sobolev trace embedding h1 lq in a bounded smooth domain can be obtained as the limit as 0 of the best constant of the usual sobolev embedding h1 lq dx where x 2 dist x is a small neighborhood of the boundary we also analyze symmetry properties of extremals of this last embedding when is a ball

lp 0 1 q plq 0 1 is spaceable for every p 0 abstract in this short note we prove the result stated in the title that is for every p 0 there exists an infinite dimensional closed linear subspace of l p 0 1 every nonzero element of which does not belong to q p l q 0 1 this answers in the positive a question raised in 2010 by r m aron on the spaceability of the above sets for both the banach and quasi banach cases we also complete some recent results from botelho et al 2011 3 for subsets of sequence spaces

nonlinear subsets of function spaces and spaceability abstract in this paper we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on 0 1 every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular we consider lorentz marcinkiewicz and orlicz spaces the answer is affirmative for marcinkiewicz spaces and negative for lorentz and orlicz spaces also the same problem is studied for nakano spaces assuming different hypothesis

algebraic structure of continuous unbounded and integrable functions abstract in this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in 0 and of the family of sequences of these functions converging to zero uniformly on compacta and in l 1 norm in addition we concentrate on the speed at which these functions grow their smoothness and the strength of their convergence to zero