on the capacity achieving distribution of the discrete time noncoherent and partially coherent awgn channels we investigate the communication limits over rapid phase varying channels and consider the capacity of a discrete time noncoherent additive white gaussian noise ncawgn channel under the average power constraint we obtain necessary and sufficient conditions for the capacity achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points using this characterization of the capacity achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions in addition we provide some easily computable lower and upper bounds on the channel capacity finally we extend some of these results to the partially coherent channel where it is assumed that a phase locked loop pll is used to track the carrier phase at the receiver and that an ideal interleaver and de interleaver are employed rendering the tikhonov distributed residual phase errors statistically independent from one symbol interval to another

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

on the moment determinance and random mixture of nakagami m variates we study complex valued nakagami m variates establishing the moment determinance of the envelope phase and joint envelope phase nakagami m probability density functions pdf s inspired by that result we then show that nakagami m variates with arbitrary fading figure m can be accurately decomposed onto a mixture of nakagami m variates with integer or half integer m i e 2m the latter has the immediate theoretical implication that results currently known to hold for nakagami m channels under the constraint 2m can accurately be extended to arbitrary m via simple linear decomposition with weights given by the random mixture probabilities for which formulas are provided the latter is illustrated with an example of the application of the random mixture decomposition to the simplification and generalization of bit error rate ber expressions for psk modulation in the nakagami m relay channel for completeness implications on possible extensions and improvements of existing methods to generate nakagami m variates is also briefly discussed in the form of further examples

majorization and a schur horn theorem for positive compact operators the nonzero kernel case abstract schur horn theorems focus on determining the diagonal sequences obtainable for an operator under all possible basis changes formally described as the range of the canonical conditional expectation of its unitary orbit following a brief background survey we prove an infinite dimensional schur horn theorem for positive compact operators with infinite dimensional kernel one of the two open cases posed recently by kaftal weiss there they characterized the diagonals of operators in the unitary orbits for finite rank or zero kernel positive compact operators here we show how the characterization problem depends on the dimension of the kernel when it is finite or infinite dimensional we obtain exact majorization characterizations of the range of the canonical conditional expectation of the unitary orbits of positive compact operators with infinite dimensional kernel unlike the approximate characterizations of arveson kadison but extending the exact characterizations of gohberg markus and kaftal weiss recent advances in this subject and related subjects like traces on ideals show the relevance of new kinds of sequence majorization as in the work of kaftal weiss e g strong majorization and another majorization similar to what here we call p majorization and of kalton sukochev e g uniform hardy littlewood majorization and of bownik jasper e g riemann and lebesgue majorization likewise key tools here are new kinds of majorization which we call p and approximate p majorization 0 p

stochastic bifurcation models we study an ordinary differential equation controlled by a stochastic process we present results on existence and uniqueness of solutions on associated local times trotter and ray knight theorems and on time and direction of bifurcation a relationship with lipschitz approximations to brownian paths is also discussed

on skew brownian motion we consider the stochastic equation x t w t beta l x 0 t where w is a standard wiener process and l x 0 cdot is the local time at zero of the unknown process x there is a unique solution x and it is adapted to the fields of w if beta leq 1 but no solutions exist if beta 1 in the former case setting alpha beta 1 2 the unique solution x is distributed as a skew brownian motion with parameter alpha this is a diffusion obtained from standard wiener process by independently altering the signs of the excursions away from zero each excursion being positive with probability alpha and negative with probability 1 alpha finally we show that skew brownian motion is the weak limit as n rightarrow infty of n 1 2 s lbrack nt rbrack where s n is a random walk with exceptional behavior at the origin

when weak and local measure convergence implies norm convergence abstract let m be a von neumann algebra of operators on a hilbert space h and be a faithful normal semifinite trace on m let t be the measure topology on the algebra s m of all measurable operators we prove that for b s m the sets i b a s m h b a b and k b a s m a a b are convex and t closed in s m in this case we have i b b t b t m h and t 1 and for invertible b we describe the set of extreme points of the set i b let m be an atomic von neumann algebra we prove that an operator b s m is compact if and only if the set i b is t compact the t compactness of i b for all compact operators b characterizes these algebras

embeddings of operator ideals into lp spaces on finite von neumann algebras abstract let l h be the algebra of all bounded operators on an infinite dimensional hilbert space h and let i i be an ideal in l h equipped with a banach norm which is distinct from the schatten von neumann ideal l p h 1 p 2 we prove that i isomorphically embeds into an l p space l p r 1 p 2 here r is the hyperfinite ii1 factor if its commutative core that is calkin space for i isomorphically embeds into l p 0 1 furthermore we prove that an orlicz ideal l m h l p h isomorphically embeds into l p r 1 p 2 if and only if it is an interpolation space for the banach couple l p h l 2 h finally we consider isomorphic embeddings of i i into l p spaces associated with arbitrary finite von neumann algebras

power correlation coefficient of a very general fading model in maximal ratio combining a very general fading scenario is considered for which exact closed form formulas for the correlation coefficient of the instantaneous power at the output of a maximal ratio combining receiver is derived the model includes the main fading environments as very particular cases it is valid for both identically and non identically distributed multipath clusters and for both stationary and nonstationary environments most interestingly the model allows for an uncountable number of combinations of novel fading scenarios a further generalization is achieved with the angle as well as the time of arrival of the waves permitted to vary throughout the multipath clusters as opposed to known models for which these parameters are fixed several particular examples illustrate the applicability of the general formulations

dixmier traces and extrapolation description of noncommutative lorentz spaces we study the connections between dixmier traces functions and traces of heat semigroups beyond the dual of the macaev ideal and in the general context of semifinite von neumann algebras we show that the correct framework for this investigation is that of operator lorentz spaces possessing an extrapolation description we demonstrate the applicability of our results to hormander weyl pseudo differential calculus on rn in this context we prove that the dixmier trace of a pseudo differential operator coincides with the dixmier integral of its symbol

ando s inequality for uniform submajorization abstract we discuss ando s inequality involving operator monotone functions and demonstrate that a natural strengthening of ando s result to uniform submajorization holds if and only if the operator monotone function has a very simple rational form

dixmier measurability in marcinkiewicz spaces and applications abstract we present new results concerning the description of dixmier measurable elements in the sense of a connes in marcinkiewicz spaces and demonstrate some applications of our results in particular we complement famous connes trace theorem by describing the asymptotics of the singular function of order n classical pseudo differential operators on an n dimensional compact riemannian manifold

weak type commutator and lipschitz estimates resolution of the nazarov peller conjecture let m be a semi finite von neumann algebra and let f r c be a lipschitz function if a b m are self adjoint operators such that a b l1 m then

self avoiding random walk a brownian motion model with local time drift a natural model for a self avoiding brownian motion inr d when specialised and simplified tod 1 becomes the stochastic differential equation x t b t int limits 0 t g x s l s x s ds where l t x t 0 x r is the local time process ofx thoughx is not markovian an analogue of the ray knight theorem holds for l x x r which allows one to prove in many cases of interest that mathop lim limits t to infty x t t exists almost surely and to identify the limit

blum hanson type ergodic theorems in noncommutative symmetric spaces we prove a version of blum hanson ergodic theorem for l1 l l1 l contractions acting in noncommutative symmetric spaces with order continuous norm a similar result is established for arbitrary contractions on hardy subspaces of p convex schatten ideals of compact operators

on the generation of tikhonov variates a novel simple and efficient method for the generation of tikhonov a k a von mises random variates is proposed in the proposed method circular variates of a prescribed tikhonov distribution pt x alpha xi are generated via the transformation of variates selected randomly on a one for one basis from a bank of k distinct cauchy and gaussian generators the mutually exclusive probabilities of sampling from each of the cauchy or gaussian generators as well as the variance and half width parameters that specify the latter are derived directly from the cauchy gaussian and tikhonov characteristic functions all of which are either known or given in closed form the proposed random mixture technique is extremely efficient in that a single pair of uniform random numbers is consumed in the generation of each tikhonov or von mises sample regardless of the prescribed concentration and centrality parameters alpha xi all requiring neither the rejection of samples nor the repetitive evaluation of computationally demanding functions additional attractive features of the method are as follows by construction the first dominant n circular moments of tikhonov variates generated with the proposed random mixture technique are the ones that best approximate their corresponding theoretical values with errors measured exactly the exact distribution of generated tikhonov variates is determined analytically and its kullback leibler divergence to the exact tikhonov pdf is shown also analytically to be negligible finally the technique establishes a connection between tikhonov and gaussian variates which can be exploited e g in the generation of piecewise continuous pseudo random functions with tikhonov distributed outcomes

the κ μ phase envelope joint distribution this paper derives an exact closed form expression for the phase envelope joint distribution of the fading environment a general fading model that includes the rice and the nakagami m models as special cases the derived joint statistics are obtained so that compatibility with both rice as well as nakagami m cases are kept monte carlo simulation plots are presented that are in accordance with the formulations developed here as a consequence of the derivation of the required pdf an interesting solution to a very general probability problem is proposed namely given the pdf of the modulus of a variate find the pdf of the variate additionally several new integral relations of the modified bessel function are given

derivations on symmetric quasi banach ideals of compact operators abstract let i j be symmetric quasi banach ideals of compact operators on an infinite dimensional complex hilbert space h let j i be the space of multipliers from i to j obviously ideals i and j are quasi banach algebras and it is clear that ideal j is a bimodule for i we study the set of all derivations from i into j we show that any such derivation is automatically continuous and there exists an operator a j i such that a moreover a 1 b h i j 2 c a j i for some complex number where c is the modulus of concavity of the quasi norm j and 1 is the identity operator on h in the special case when i j k h is a symmetric banach ideal of compact operators on h our result yields the classical fact that any derivation on k h may be written as a where a is some bounded operator on h and a b h i i 2 a b h

design of turbo coded modulation for the awgn channel with tikhonov phase error we design 1 b symbol hz parallel concatenated turbo coded modulation pctcm for the additive white gaussian noise awgn channel with tikhonov phase error constituent recursive convolutional codes are optimized so that the turbo codes have low error floors and low convergence thresholds the pairwise error probability based on the maximum likelihood decoding metric is used to select codes with low error floors we also present a gaussian approximation method that accurately predicts convergence thresholds for pctcm codes on the awgn tikhonov channel simulation results show that the selected codes perform within 0 6 db of constellation constrained capacity and have no detectable error floor down to bit error rates of 10 sup 6

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

which traces are spectral abstract among ideals of compact operators on a hilbert space we identify a subclass of those closed with respect to the logarithmic submajorization within this subclass we answer the questions asked by pietsch 22 and by dykema figiel weiss and wodzicki 7 in the first case we show that lidskii type formulae hold for every trace on such ideal in the second case we provide the description of the commutator subspace associated with a given ideal finally we prove that a positive trace on an arbitrary ideal is spectral if and only if it is monotone with respect to the logarithmic submajorization

orlicz spaces with convexity or concavity constant one abstract we characterize the classes of function and sequence orlicz spaces that satisfy upper or lower p estimate with constant one we also present a characterization of p convexity or p concavity with constant one in orlicz spaces

complete characterization of hadamard powers preserving loewner positivity monotonicity and convexity abstract entrywise powers of symmetric matrices preserving positivity monotonicity or convexity with respect to the loewner ordering arise in various applications and have received much attention recently in the literature following fitzgerald and horn 1977 8 it is well known that there exists a critical exponent beyond which all entrywise powers preserve positive definiteness similar phenomena have also recently been shown by hiai 2009 to occur for monotonicity and convexity in this paper we complete the characterization of all the entrywise powers below and above the critical exponents that are positive monotone or convex on the cone of positive semidefinite matrices we then extend the original problem by fully classifying the positive monotone or convex powers in a more general setting where additional rank constraints are imposed on the matrices we also classify the entrywise powers that are super sub additive with respect to the loewner ordering finally we extend all the previous characterizations to matrices with negative entries our analysis consequently allows us to answer a question raised by bhatia and elsner 2007 regarding the smallest dimension for which even extensions of the power functions do not preserve loewner positivity

local time flow related to skew brownian motion burdzy s research partially supported by nsf grant dms 9700721 chen s research partially supported by nsa grant mda904 99 1 0104

traces of compact operators and the noncommutative residue abstract we extend the noncommutative residue of m wodzicki on compactly supported classical pseudo differential operators of order d and generalise a connes trace theorem which states that the residue can be calculated using a singular trace on compact operators contrary to the role of the noncommutative residue for the classical pseudo differential operators a corollary is that the pseudo differential operators of order d do not have a unique trace pseudo differential operators can be non measurable in connes sense other corollaries are given clarifying the role of dixmier traces in noncommutative geometry including the definitive statement of connes original theorem

on power bounded operators in finite von neumann algebras abstract it is proved that any power bounded operator of class c 1 in a finite von neumann algebra is conjugate to a unitary this solves a conjecture stated by i kovacs in 1970 an important ingredient of the proof is the study of completely positive projections on some operator space

martingale inequalities in noncommutative symmetric spaces abstract we provide generalizations of burkholder s inequalities involving conditioned square functions of martingales to the general context of martingales in noncommutative symmetric spaces more precisely we prove that burkholder s inequalities are valid for any martingale in noncommutative space constructed from a symmetric space defined on the interval 0 with the fatou property and whose boyd indices are strictly between 1 and 2 this answers positively a question raised by jiao and may be viewed as a conditioned version of similar inequalities for square functions of noncommutative martingales using duality we also recover the previously known case where the boyd indices are finite and are strictly larger than 2

noncommutative khintchine inequalities in interpolation spaces of lp spaces abstract we prove noncommutative khintchine inequalities for all interpolation spaces between l p and l 2 with p 2 in particular it follows that khintchine inequalities hold in l 1 using a similar method we find a new deterministic equivalent for the rc norm in all interpolation spaces between l p spaces which unifies the cases p 2 and p 2 it produces a new proof of khintchine inequalities for p 1 for free variables to complete the picture we exhibit counter examples which show that neither of the usual closed formulas for khintchine inequalities can work in l 2 we also give an application to martingale inequalities

johnson schechtman inequalities in the free probability theory abstract we introduce and study a free kruglov operator as an application of this study we prove an analogue of the johnson schechtman inequalities in the setting of free probability theory and an arbitrary symmetric operator space this extends and complements earlier l p results of junge et al 2007 12

rademacher averages on noncommutative symmetric spaces let e be a separable or the dual of a separable symmetric function space let m be a semifinite von neumann algebra and let e m be the associated noncommutative function space let ek k 1 be a rademacher sequence on some probability space for finite sequences xk k 1 of e m we consider the rademacher averages kek xk as elements of the noncommutative function space e l m and study estimates for their norms kek xk e calculated in that space we establish general khintchine type inequalities in this context then we show that if e is 2 concave kek xk e is equivalent to the infimum of yk yk 12 zkzk 12 over all yk zk in e m such that xk yk zk for any k 1 dual estimates are given when e is 2 convex and has a nontrivial upper boyd index in this case kek xk e is equivalent to xk xk 12 xkxk 12 we also study rademacher averages i jei ej xij for doubly indexed families xij i j of e m

multiplication operators on non commutative spaces abstract boundedness and compactness properties of multiplication operators on quantum non commutative function spaces are investigated for endomorphic multiplication operators these properties can be characterized in the setting of quantum symmetric spaces for non endomorphic multiplication operators these properties can be completely characterized in the setting of quantum l p spaces and a partial solution obtained in the more general setting of quantum orlicz spaces

norm inequalities related to operator monotone functions let a b be positive semidefinite matrices and cdot any unitarily invariant norm on the space of matrices we show f a f b geq f a b for any non negative operator monotone function f t on 0 infty and g a g b leq g a b for non negative increasing function g t on 0 infty with g 0 0 and g infty infty whose inverse function is operator monotone

johnson schechtman inequalities for noncommutative martingales abstract in this paper we study johnson schechtman inequalities for noncommutative martingales more precisely disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space e m of a finite von neumann algebra m without making any assumption on the boyd indices of e we show that we can obtain johnson schechtman inequalities for arbitrary martingale difference sequences and that in contrast with the classical case of independent random variables or the noncommutative case of freely independent random variables the inequalities are one sided except when e l 2 0 1 as an application we partly resolve a problem stated by randrianantoanina and wu in 46 we also show that we can obtain sharp moment analogues for orlicz functions satisfying p convexity and q concavity for 1 p 2 q 2 and p 2 2 q this is new even for the classical case we also extend and strengthen the noncommutative burkholder gundy inequalities in symmetric spaces and in the moment case

generalized hermitian operators in this paper the concept of generalized hermitian operators defined on a complex hilbert space is introduced it is shown that the spectrums and the fredholm fields of generalized hermitian operators are both symmetric with respect to the real axis some other results on generalized hermitian operators are obtained

the optimal range of the calderon operator and its applications abstract we identify the optimal range of the calderon operator and that of the classical hilbert transform in the class of symmetric quasi banach spaces further consequences of our approach concern the optimal range of the triangular truncation operator operator lipschitz functions and commutator estimates in ideals of compact operators

commutator estimates in w algebras abstract let m be a w algebra and let ls m be the algebra of all locally measurable operators affiliated with m it is shown that for any self adjoint element a ls m there exists a self adjoint element c 0 from the center of ls m such that for any e 0 there exists a unitary element u e from m satisfying a u e 1 e a c 0 a corollary of this result is that for any derivation on m with the range in a not necessarily norm closed ideal i m the derivation is inner that is a a and a i similar results are also obtained for inner derivations on ls m

complex uniform rotundity in symmetric spaces of measurable operators abstract let m be a semifinite von neumann algebra with a faithful normal semifinite trace and e be a symmetric banach function space on 0 1 we show that e is complex uniformly rotund if and only if e m is complex uniformly rotund moreover under the assumption that e is p convex for some p 1 complex uniform rotundity of e implies complex uniform rotundity of e m therefore if e has non trivial convexity complex uniform convexity of e is equivalent with complex uniform convexity of e m we obtain an analogous result for the unitary matrix space c e and a symmetric banach sequence space e from the above we conclude that e m is complex uniformly rotund if and only if its norm e m is uniformly monotone

fine mesh limit of the vrjp in dimension one and bass burdzy flow we introduce a continuous space limit of the vertex reinforced jump process vrjp in dimension one which we call linearly reinforced motion lrm on mathbb r it is constructed out of a convergent bass burdzy flow the proof goes through the representation of the vrjp as a mixture of markov jump processes as a by product this gives a representation in terms of a mixture of diffusions of the lrm and of the bass burdzy flow itself we also show that our continuous space limit can be obtained out of the edge reinforced random walk errw since the errw and the vrjp are known to be closely related compared to the discrete space processes the lrm has an additional symmetry in the initial local times initial occupation profile changing them amounts to a deterministic change of the space and time scales

fast equilibrium selection by rational players living in a changing world we study a coordination game with randomly changing payoffs and small frictions in changing actions using only backwards induction we find that players must coordinate on the risk dominant equilibrium more precisely a continuum of fully rational players are randomly matched to play a symmetric 2 x 2 game the payoff matrix changes according to a random walk players observe these payoffs and the population distribution of actions as they evolve the game has frictions opportunities to change strategies arrive from independent random processes so that the players are locked into their actions for some time as the frictions disappear each player ignores what the others are doing and switches at her first opportunity to the risk dominant action history dependence emerges in some cases when frictions remain positive

a stochastic flow arising in the study of local times a stochastic flow of homeomorphisms of open image in new window previously studied by bass and burdzy 2 and hu and warren 4 is shown to arise in the study of the local times of brownian motion this leads to a new proof of the ray knight theorems for the flow via the classical ray knight theorems for brownian motion

local invariance principles and their application to density estimation letx 1 x n be independent random variables with uniform distribution over 0 1 d andx n be the centered and normalized empirical process associated tox 1 x n given a vapnik chervonenkis classl of bounded functions from 0 1 d intor of bounded variation we apply the one dimensional dyadic scheme of komlos major and tusnady to get the best possible rate in dudley s uniform central limit theorem for the empirical process e n h h l whenl fulfills some extra condition we prove there exists some sequenceb n of brownian bridges indexed byl such that wherek l denotes the maximal variation of the elements ofl this result is then applied to maximal deviations distributions for kernel density estimators under minimal assumptions on the sequence of bandwith parameters we also derive some results concerning strong approximations for empirical processes indexed by classes of sets with uniformly small perimeter for example it follows from beck s paper that the above result is optimal up to a possible factor sqrt log n whenl is the class of euclidean balls with radius less thanr

rosenthal inequalities in noncommutative symmetric spaces abstract we give a direct proof of the upper khintchine inequality for a noncommutative symmetric quasi banach function space with nontrivial upper boyd index this settles an open question of c le merdy and the fourth named author le merdy and sukochev 2008 24 we apply this result to derive a version of rosenthal s theorem for sums of independent random variables in a noncommutative symmetric space as a result we obtain a new proof of rosenthal s theorem for haagerup l p spaces

canonical systems with discrete spectrum abstract we study spectral properties of two dimensional canonical systems y t z j h t y t t a b where the hamiltonian h is locally integrable on a b positive semidefinite and weyl s limit point case takes place at b we answer the following questions explicitly in terms of h is the spectrum of the associated selfadjoint operator discrete if it is discrete what is its asymptotic distribution here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast making an analogy with complex analysis this corresponds to convergence class and type w r t proximate orders having order larger than 1 it is a surprising fact that these properties depend only on the diagonal entries of h in 1968 l de branges posed the following question as a fundamental problem which hamiltonians are the structure hamiltonian of some de branges space we give a complete and explicit answer

poincare type inequalities for group measure spaces and related transportation cost inequalities let g be a countable discrete group with an orthogonal representation on a real hilbert space h we prove lp poincare inequalities for the group measure space l h g where both the group action and the gaussian measure space h are associated with the representation the idea of proof comes from pisier s method on the boundedness of riesz transform and lust piquard s work on spin systems then we deduce a transportation type inequality from the lp poincare inequalities in the general noncommutative setting this inequality is sharp up to a constant in the gaussian setting several applications are given including wiener rademacher chaos estimation and new examples of rieffel s compact quantum metric spaces

noncommutative kothe duality using techniques drawn from the classical theory of rearrangement invariant banach function spaces we develop a duality theory in the sense of kothe for symmetric banach spaces of measurable operators affiliated with a semifinite von neumann algebra equipped with a distinguished trace a principal result of the paper is the identification of the kothe dual of a given banach space of measurable operators in terms of normality

quasisimilarity of power bounded operators and blum hanson property abstract we construct a power bounded operator on a hilbert space which is not quasisimilar to a contraction to this aim we solve an open problem from operator ergodic theory showing that there are power bounded hilbert space operators without the blum hanson property we also find an example of a power bounded operator quasisimilar to a unitary operator which is not similar to a contraction thus answering negatively open questions raised by kerchy and cassier on the positive side we prove that contractions on l p spaces 1 p possess the blum hanson property

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

twisting non commutative lp spaces abstract the paper makes the first steps into the study of extensions twisted sums of noncommutative l p spaces regarded as banach modules over the underlying von neumann algebra m our approach combines kalton s description of extensions by centralizers these are certain maps which are in general neither linear nor bounded with a general principle due to rochberg and weiss saying that whenever one finds a given banach space y as an intermediate space in a complex interpolation scale one automatically gets a self extension 0 y x y 0 for semifinite algebras considering l p l p m as an interpolation space between m and its predual m one arrives at a certain self extension of l p that is a kind of noncommutative kalton peck space and carries a natural bimodule structure some interesting properties of these spaces are presented for general algebras including those of type iii the interpolation mechanism produces two rather than one extensions of one sided modules one of left modules and the other of right modules whether or not one may find nontrivial self extensions of bimodules in all cases is left open

logarithmic submajorisation and order preserving linear isometries abstract let e and f be noncommutative operator spaces affiliated with semifinite von neumann algebras m 1 and m 2 respectively we establish a noncommutative version of abramovich s theorem 1 which provides the general form of normal order preserving linear operators t e i n t o f having the disjointness preserving property as an application we obtain a noncommutative huijsmans wickstead theorem 44 by establishing the disjointness preserving property for an order preserving isometry t e f from a noncommutative symmetrically normed in particular quasi normed space into another we obtain the existence of a jordan monomorphism from m 1 into m 2 and the general form of this isometry which extends and complements a number of existing results such as 12 theorem 1 67 corollary 1 72 theorem 2 and 15 theorem 3 1 in particular we fully resolve the case when f is the predual of m 2 and other untreated cases in 78

dixmier traces are weak dense in the set of all fully symmetric traces abstract we extend dixmier s construction of singular traces see 2 to arbitrary fully symmetric operator ideals in fact we show that the set of dixmier traces is weak dense in the set of all fully symmetric traces that is those traces which respect hardy littlewood submajorization our results complement and extend earlier work of wodzicki 22

optimal switching between a pair of brownian motions consider two brownian motions b 1 s1 and b 2 s2 each taking values on an interval 0 a i i 1 2 with absorption at the endpoints we can alternate between letting b 1 s1 run while freezing b 2 s2 and letting b 2 s2 run while freezing b 1 s1 this results in a swtiched process that evolves in the rectangle d 0 a 1 0 a 2 like a horizontal brownian motion when b 2 s2 freezes and like a vertical brownian motion when b 1 s1 freezes let f x 1 x 2 be a nonnegative continuous payoff function defined on the boundary d of d a control consists of a switching strategy and a stopping time we study the problem of finding an optimal control which maximizes the expected payoff obtained at time stopping in the interior results in zero reward

continuous derivations on algebras of locally measurable operators are inner it is proved that every continuous derivation on the algebra s m of all measurable operators affiliated with a von neumann algebra m is inner for every properly infinite von neumann algebra m any derivation on the algebra s m is inner

derivations with values in ideals of semifinite von neumann algebras let m be a semifinite von neumann algebra with a faithful semifinite normal trace and let a be an arbitrary c subalgebra of m assume that e is a fully symmetric function space on 0 having fatou property and order continuous norm and e m is the corresponding symmetric operator space we prove that every derivation a e m e m m is inner strengthening earlier results by kaftal and weiss 28 in the case when m is a semifinite non finite factor we show that our assumptions on e 0 are sharp

non commutative banach function spaces in this paper we survey some aspects of the theory of non commutative banach function spaces that is spaces of measurable operators associated with a semi finite von neumann algebra these spaces are also known as non commutative symmetric spaces the theory of such spaces emerged as a common generalization of the theory of classical commutative rearrangement invariant banach function spaces in the sense of w a j luxemburg and a c zaanen and of the theory of symmetrically normed ideals of bounded linear operators in hilbert space in the sense of i c gohberg and m g krein these two cases may be considered as the two extremes of the theory in the first case the underlying von neumann algebra is the commutative algebra l on some measure space with integration as trace in the second case the underlying von neumann algebra is b the algebra of all bounded linear operators on a hilbert space with standard trace important special cases of these non commutative spaces are the non commutative l p spaces which correspond in the commutative case with the usual l p spaces on a measure space and in the setting of symmetrically normed operator ideals they correspond to the schatten p classes mathfrak s p

interpolation between l_0 mathcal m tau l 0 m τ and l_ infty mathcal m tau l m τ let mathcal m be a semifinite von neumann algebra with a faithful semifinite normal trace tau we show that the symmetrically delta normed operator space e mathcal m tau corresponding to an arbitrary symmetrically delta normed function space e 0 infty is an interpolation space between l 0 mathcal m tau and mathcal m which is in contrast with the classical result that there exist symmetric operator spaces e mathcal m tau which are not interpolation spaces between l 1 mathcal m tau and mathcal m besides we show that the mathcal k functional of every x in l 0 mathcal m tau mathcal m coincides with the mathcal k functional of its generalized singular value function mu x several applications are given e g it is shown that the pair l 0 mathcal m tau mathcal m is mathcal k monotone when mathcal m is a non atomic finite factor