on the existence of local observables in theories with a factorizing s matrix the scaling limit of the two dimensional ising model above the critical temperature is considered as an example for relativistic quantum theories on two dimensional minkowski space exhibiting a factorizing s matrix in this model a recently proposed criterion for the existence of local quantum field theories with a prescribed factorizing scattering matrix is verified thereby establishing a new constructive approach to two dimensional quantum field theory in a particular example the existence proof is accomplished by analysing the nuclearity properties of certain specific subsets of fermionic fock spaces and yields as a byproduct also a verification of the energy nuclearity condition of buchholz and wichmann in models of free fermions in four spacetime dimensions

applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

on the continuity of the map ϑ ϑ from the predual of a w algebra abstract let be elements in the predual of a w algebra for their absolute value parts the estimate 2 1 2 is obtained

perturbations of kms states and noncommutative lp spaces we extend the theory of perturbations of kms states to a class of unbounded perturbations using noncommutative lp spaces we also prove certain stability of the domain of the modular operator associated with a p continuous state this allows us to define an analytic multiple time kms condition and to obtain its analyticity together with some bounds to its norm we extend the theory of perturbations of kms states to a class of unbounded perturbations using noncommutative lp spaces we also prove certain stability of the domain of the modular operator associated with a p continuous state this allows us to define an analytic multiple time kms condition and to obtain its analyticity together with some bounds to its norm

crossed products extensions of lp bounds for amenable actions abstract we will extend earlier transference results due to neuwirth and ricard from the context of noncommutative l p spaces associated with amenable groups to that of noncommutative l p spaces associated with crossed products of amenable actions namely if m g c is a completely bounded fourier multiplier on l p then it extends to the crossed product with similar bounds provided that the action is amenable and trace preserving furthermore our construction also allows to extend g equivariant completely bounded operators acting on the space part to the crossed product provided that the generalized folner sets of the action satisfy certain accretivity property as a corollary we obtain stability results for maximal l p bounds over crossed products we derive using that stability results an application to the boundedness of smooth multipliers in the l p spaces of group algebras

the hausdorff young inequality on lie groups we prove several results about the best constants in the hausdorff young inequality for noncommutative groups in particular we establish a sharp local central version for compact lie groups and extend known results for the heisenberg group in addition we prove a universal lower bound to the best constant for general lie groups

c algebras and automorphism groups let a g be ac dynamical system withg a topological group let be a representation ofa we will show that there exists a quasiequivalent representation hat pi to which is a covariant representation if and only if the folium of is invariant under the action ofg and this action is strongly continuous

norm inequalities for the absolute value of hilbert space operators we use norm inequalities for operators such as cauchy schwarz inequality and minkowski inequality to establish sharp norm inequalities for the absolute value of operators among other inequalities it is shown that if a b and x are operators on a hilbert space such that x is self adjoint and r 1 then this inequality generalizes some earlier related results other related inequalities are also discussed

commuting self adjoint extensions of symmetric operators defined from the partial derivatives we consider the problem of finding commuting self adjoint extensions of the partial derivatives 1 i xj j 1 d with domain cc where the self adjointness is defined relative to l2 and is a given open subset of rd the measure on is lebesgue measure on rd restricted to the problem originates with segal and fuglede and is difficult in general in this paper we provide a representation theoretic answer in the special case when i 2 and i is an open interval we then apply the results to the case when is a d cube id and we describe possible subsets rd such that e id is an orthonormal basis in l2 id

isometries of non commutative lorentz spaces on determine la forme generale d une isometrie positive d un espace symetrique non commutatif sur un espace totalement symetrique non commutatif on decrit toutes les isometries d un espace de lorentz non commutatif

fields over unsharp coordinates it has been shown that space time coordinates can exhibit only very few types of short distance structures if described by linear operators they can be continuous discrete or unsharp in one of two ways in the literature various quantum gravity models of space time at short distances point towards one of these two types of unsharpness here we investigate the properties of fields over such unsharp coordinates we find that these fields are continuous but possess only a finite density of degrees of freedom similar to fields on lattices as a special case we recover the shannon sampling theorem of information theory

dirichlet forms and markovian semigroups on standard forms of von neumann algebras we characterize w continuous markovian semigroups on a von neumann algebra m which are 0 symmetric w r t a faithful normal state 0in m in terms of quadratic forms on the hilbert space h of a standard form m h p j we characterize also symmetric strongly continuous contraction semigroups on a real hilbert space h which leave invariant a closed convex set in h in terms of a contraction property of the associated quadratic forms we apply the results to give criteria of essential selfadjointness for quadratic form sums and to give a characterization of w continuous markovian semigroups on m which commute with the modular automorphism group 0t

noncommutative lp structure encodes exactly jordan structure abstract we prove that for all 1 p p 2 the l p spaces associated to two von neumann algebras m n are isometrically isomorphic if and only if m and n are jordan isomorphic this follows from a noncommutative l p banach stone theorem a specific decomposition for surjective isometries of noncommutative l p spaces

fractional powers on noncommutative lp for p 1 abstract we prove that the homogeneous functional calculus associated to x x or x sgn x x for 0 1 is holder on selfadjoint elements of noncommutative l p spaces for 0 p with values in l p this extends an inequality of birman koplienko and solomjak also obtained by ando

uncertainty principles for locally compact quantum groups abstract in this paper we prove the donoho stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi shifts of group like projections we also prove the hirschman beckner uncertainty principle for compact quantum groups and discrete quantum groups furthermore we show hardy s uncertainty principle for locally compact quantum groups in terms of bi shifts of group like projections

on subspaces of non commutative lp spaces abstract we study some structural aspects of the subspaces of the non commutative haagerup l p spaces associated with a general non necessarily semi finite von neumann algebra if a subspace x of l p contains uniformly the spaces l p n n 1 it contains an almost isometric almost 1 complemented copy of l p if x contains uniformly the finite dimensional schatten classes s p n it contains their l p direct sum too we obtain a version of the classical kadec pelczynski dichotomy theorem for l p spaces p 2 we also give operator space versions of these results the proofs are based on previous structural results on the ultrapowers of l p together with a careful analysis of the elements of an ultrapower l p u which are disjoint from the subspace l p these techniques permit to recover a recent result of n randrianantoanina concerning a subsequence splitting lemma for the general non commutative l p spaces various notions of p equiintegrability are studied one of which is equivalent to randrianantoanina s one and some results obtained by haagerup rosenthal and sukochev for l p spaces based on finite von neumann algebras concerning subspaces of l p containing l p are extended to the general case

construction of quantum field theories with factorizing s matrices the subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two dimensional minkowski space employing the algebraic framework of quantum field theory it is shown under which conditions an algebra of observables localized in a wedge shaped region of spacetime can be used to construct model theories a crucial input in this context is the modular nuclearity condition for wedge algebras which implies the existence of local observables as an application of the new method a rigorous construction of a large family of models with factorizing s matrices is obtained in an inverse scattering approach a given factorizing scattering operator is used to define certain semi localized wightman fields associated to it with the help of these fields a wedge algebra can be defined which determines the local observable content of a well defined quantum field theory in this approach the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge local observables these conditions are shown to hold for a large class of underlying s matrices including the scattering operators of the sinh gordon model and the scaling ising model as special examples the so constructed models are investigated with respect to their scattering properties they are shown to solve the inverse scattering problem for the underlying s matrices and a proof of asymptotic completeness for these models is given

canonical extension of actions of locally compact quantum groups abstract in this paper we generalize the notion of the canonical extension of automorphisms of von neumann algebras to the case of actions of locally compact quantum groups in the sense of kustermans and vaes various expected properties will be shown to hold for this new canonical extension as an application we describe the flow of weights of the crossed product of a type iii factor by some special action of a discrete kac algebra

causal independence and the energy level density of states in local quantum field theory within the general framework of local quantum field theory a physically motivated condition on the energy level density of well localized states is proposed and discussed it is shown that any model satisfying this condition obeys a strong form of the principle of causal statistical independence which manifests itself in a specific algebraic structure of the local algebras split property it is also shown that the proposed condition holds in a free field theory

an inequality for hilbert schmidt norm for the absolute value c c c 1 2 and the hilbert schmidt norm c hs trc c 1 2 of an operatorc the following inequality is proved for any bounded linear operatorsa andb on a hilbert space a b hs leqq 2 1 2 a b hs the corresponding inequality for two normal state and of a von neumann algebram is also proved in the following form d varphi psi leqq xi varphi xi psi leqq 2 1 2 d varphi psi here denotes the unique vector representative of a state in a natural positive conep form andd denotes the bures distance defined as the infimum which is also the minimum of the distance of vector representatives of and in particular xi varphi 1 xi varphi 2 leqq 2 1 2 xi 1 xi 2 for any vector representatives j of j j 1 2

the non commutative flow of weights on a von neumann algebra abstract the flow of weights of connes and takesaki is a canonical functor from the category of separable factors to the category of ergodic flows the non commutative flow of weights is another canonical functor from the category of separable factors to the category of covariant systems of semi finite von neumann algebras equipped with trace scaling one parameter automorphism groups with conjugations as morphisms the constructions of these two functors are very similar the flow of weights functor is obtained by looking at all semi finite normal weights on a factor with the murray von neumann equivalence relation the non commutative flow of weights functor is obtained by relating an arbitrary pair of faithful semi finite normal weights by the connes cocycle not only does this construction put a period to the search for a canonical construction of the core of a factor of type iii but it also allows us to put the characteristic square of a factor obtained by katayama sutherland and takesaki in a new perspective the power of this new approach is seen in an ultimate solution to a long standing question of extending the extended modular automorphism of a dominant weight to an arbitrary weight which has been left open ever since the introduction of extended modular automorphisms by connes and takesaki over 20 years ago the construction of the functor ties together the theory of l p spaces of haagerup kosaki hilsum terp and izumi to the structure theory of a factor of type iii in fact the non commutative flow of weights is obtained by the analytic continuation of l p spaces to a pure imaginary value of p

algebraic tensor products and internal homs of noncommutative lp spaces abstract we prove that the multiplication map is an isometric isomorphism of quasi banach m m bimodules here is the noncommutative l p space of an arbitrary von neumann algebra m and m denotes the algebraic tensor product over m equipped with the quasi projective tensor norm but without any kind of completion similarly the left multiplication map is an isometric isomorphism of quasi banach m m bimodules where hom m denotes the algebraic internal hom in particular we establish an automatic continuity result for such maps applications of these results include establishing explicit algebraic equivalences between the categories of modules of junge and sherman for all p 0 as well as identifying subspaces of the space of bilinear forms on spaces this paper is also available at arxiv 1309 7856v2

homogeneous manifolds from noncommutative measure spaces abstract let m be a finite von neumann algebra with a faithful normal trace in this paper we study metric geometry of homogeneous spaces o of the unitary group u m of m endowed with a finsler quotient metric induced by the p norms of x p x p 1 p p 1 the main results include the following the unitary group carries on a rectifiable distance d p induced by measuring the length of curves with the p norm if we identify o as a quotient of groups then there is a natural quotient distance d p that metrizes the quotient topology on the other hand the finsler quotient metric defined in o provides a way to measure curves and therefore there is an associated rectifiable distance d o p we prove that the distances d p and d o p coincide based on this fact we show that the metric space o d p is a complete path metric space the other problem treated in this article is the existence of metric geodesics or curves of minimal length in o we give two abstract partial results in this direction the first concerns the initial values problem and the second the fixed endpoints problem we show how these results apply to several examples in the process we improve some results about the metric geometry of u m with the p norm

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

covariant information density cutoff in curved space time in information theory the link between continuous information and discrete information is established through well known sampling theorems sampling theory explains for example how frequency filtered music signals are reconstructible perfectly from discrete samples in this letter sampling theory is generalized to pseudo riemannian manifolds this provides a new set of mathematical tools for the study of space time at the planck scale theories formulated on a differentiable space time manifold can be equivalent to lattice theories there is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity

majorizations and inequalities in matrix theory abstract in matrix theory majorization plays a significant role for instance majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities this survey article is intended as a review of recent results in matrix theory related to majorization

wkb approximation in deformed space with minimal length the wkb approximation for deformed space with minimal length is considered the bohr sommerfeld quantization rule is obtained a new interesting feature in the presence of deformation is that the wkb approximation is valid for intermediate quantum numbers and can be invalid for small as well as very large quantum numbers the correctness of the rule is verified by comparing obtained results with exact expressions for corresponding spectra

nuclear maps and modular structures i general properties abstract we establish a correspondence between the split property of inclusions a b of von neumann algebras and nuclearity properties of the natural embeddings p l a lp b p 1 2 given by the modular theory

a reduction method for noncommutative l_p spaces and applications we consider the reduction of problems on general noncommutative l p spaces to the corresponding ones on those associated with finite von neumann algebras the main tool is an unpublished result of the first named author which approximates any noncommutative l p space by tracial ones we show that under some natural conditions a map between two von neumann algebras extends to their crossed products by a locally compact abelian group or to their noncommutative l p spaces we present applications of these results to the theory of noncommutative martingale inequalities by reducing most recent general noncommutative martingale ergodic inequalities to those in the tracial case

matrix factorizations and their perturbations there are several ways in which a matrix can be factorized as a product of two special matrices these factorizations are often used in numerical analysis and many perturbation bounds useful in such analysis have been proved by various authors in this paper a simple method which leads to these results and several new ones is discussed in the last section related results on the lipschitz continuity of the matrix absolute value are surveyed

schur and fourier multipliers of an amenable group acting on non commutative l p spaces consider a completely bounded fourier multiplierof a locally compact group g and take 1 p one can associate toa schur multiplier on the schatten classes sp l 2 g as well as a fourier multiplier on l p lg the non commutative l p space of the group von neumann algebra of g we prove that the completely bounded norm of the schur multiplier is not greater than the completely bounded norm of the l p fourier multiplier when g is amenable we show that equality holds extending a result by neuwirth and ricard to non discrete groups for a discrete group g and in the special case when p 6 2 is an even integer we show the following if there exists a map between l p lg and an ultraproduct of l p m sp l 2 g that intertwines the fourier multiplier with the schur multiplier then g must be amenable this is an obstruction to extend the neuwirth ricard result to non amenable groups

quantum f divergences in von neumann algebras i standard f divergences we make a systematic study of standard f divergences in general von neumann algebras an important ingredient of our study is to extend kosaki s variational expression of the relative entropy to an arbitrary standard f divergence from which most of the important properties of standard f divergences follow immediately in a similar manner we give a comprehensive exposition on the renyi divergence in von neumann algebras some results on relative hamiltonians formerly studied by araki and donald are improved as a by product we make a systematic study of standard f divergences in general von neumann algebras an important ingredient of our study is to extend kosaki s variational expression of the relative entropy to an arbitrary standard f divergence from which most of the important properties of standard f divergences follow immediately in a similar manner we give a comprehensive exposition on the renyi divergence in von neumann algebras some results on relative hamiltonians formerly studied by araki and donald are improved as a by product

complemented subspaces of spaces of multilinear forms and tensor products abstract among other things we show that l q is isomorphic to a complemented subspace of the space of multilinear forms on l p 1 l p n where q 1 is given by 1 p 1 1 p n 1 q 1 the proof strongly depends on the l module structure of the spaces l p

polynomials in operator space theory the aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces for this purpose we take advantage of the basic fact that the space pm e of all m homogeneous polynomials on a vector space e can be identified with the algebraic dual of the m th symmetric tensor product m se given an operator space v we study several different types of completely bounded polynomials on v which form the operator space duals of m sv endowed with related operator structures of special interest are what we call haagerup kronecker and schur polynomials polynomials associated with different types of matrix products

complemented subspaces of spaces of multilinear forms and tensor products ii noncommutative lp spaces abstract we study tensor products of the schatten classes s p and their duals it is shown that if p 1 1 p k 1 q 1 1 then the space of multilinear forms b s p 1 s p k c contains a complemented subspace isometric to s q we construct explicit embeddings of s r n into s p n s q n for r 1 p 1 q 1 whose range is complemented by a natural norm one projection as a byproduct we compute the nuclear norm of some multiplication operators if r 1 1 p 1 q 1 with p q 1 then given an n by n matrix the nuclear norm of the multiplication operator h s p n h s q n is n times the norm of in s r n where r max 1 r a number of results on general noncommutative l p spaces are also included

canonical operator space structures on non commutative lp spaces we analyze canonical operator space structures on the non commutative lp spaces lp m constructed by interpolation a la stein weiss based on two normal semifinite faithful weights on a w algebra m we show that there is only one canonical i e arising by interpolation operator space structure on lp m when m and p are kept fixed namely for any n s f weights on m and 0 1 the spaces lp m are all completely isomorphic when they are canonically considered as operator spaces finally we also describe the norms on all matrix spaces mn lp m which determine such a canonical quantized structure

lipschitz continuity of the absolute value and riesz projections in symmetric operator spaces a principal result of the paper is that ifeis a symmetric banach function space on the positive half line with the fatou property then for all semifinite von neumann algebras m the absolute value mapping is lipschitz continuous on the associated symmetric operator spacee m with lipschitz constant depending only oneif and only ifehas non trivial boyd indices it follows that if m is any von neumann algebra then the absolute value map is lipschitz continuous on the corresponding haageruplp space provided 1 p

pointwise tensor products of function spaces abstract by means of a mixture of linear and nonlinear techniques the paper treats quasi banach function spaces as l modules and studies the basic algebraical constructions and their interactions placing the emphasis on tensor products sample result if 0 y x z 0 is an exact sequence of l modules and homomorphisms where y and z are function spaces and v is another function space then the tensorized sequence 0 y v x v z v 0 is exact too

modular theory for bimodules abstract modular theory is developed for bimodules and its basic properties are established among them frobenius reciprocity is obtained in a fairly general setting

function spaces obeying a time varying bandlimit abstract motivated by applications to signal processing and mathematical physics recent work on the concept of time varying bandwidth has produced a class of function spaces which generalize the paley wiener spaces of bandlimited functions any regular simple symmetric linear transformation with deficiency indices 1 1 is naturally represented as multiplication by the independent variable in one of these spaces we explicitly demonstrate the equivalence of this model for such linear transformations to several other functional models based on the theories of meromorphic model spaces of hardy space and purely atomic herglotz measures on the real line respectively this theory provides a precise notion of a time varying or local bandwidth and we describe how it may be applied to construct signal processing techniques that are adapted to signals obeying a time varying bandlimit

testing the normality assumption in multivariate simultaneous limited dependent variable models abstract a diagnostic for multivariate non normality expressed as a multivariate edgeworth distribution truncated at the fourth order is presented for a multivariate simultaneous equation system in normally distributed latent variables subject to a general censoring scheme the information matrix test statistic also presented tests for multivariate non normality and particular forms of multivariate heteroskedasticity and heterocliticity alternative c tests are also suggested

non commutative orlicz spaces associated to a modular on τ measurable operators abstract in this paper we consider non commutative orlicz spaces as modular spaces and show that they are complete with respect to their modular we prove some convergence theorems for measurable operators and deal with uniform convexity of non commutative orlicz spaces

remarks on complemented subspaces of von neumann algebras in this note we include two remarks about bounded not necessarily contractive linear projections on a von neumann algebra we show that if m is a von neumann subalgebra of b h which is complemented in b h and isomorphic to m m then m is injective or equivalently m is contractively complemented we do not know how to get rid of the second assumption on m in the second part we show that any complemented reflexive subspace of a c algebra is necessarily linearly isomorphic to a hilbert space