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

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

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

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

blind decision feedback equalization of time varying channels with dpsk inputs this paper presents a new method to the blind equalization of a class of linear time varying mobile channels for differentially encoded channel input signals through reparameterization the equivalent discrete system can be modeled as a single input multiple output system unlike some existing methods this new algorithm does not require prior knowledge on the cyclic frequency of the channel response the algorithm is simple and relies only on a decision feedback structure and the differential encoding nature of the channel input signals the convergence analysis of the decision feedback system is presented along with simulation examples

asymptotic relations among fourier coefficients of automorphic eigenfunctions a detailed stationary phase analysis is presented for noncompact parameter ranges of the family of elementary eigenfunctions on the hyperbolic plane z y 1 2 k ir 2 my e 2 imx z x iy r 2 the eigenvalue s 2 m 1 2 and k ir the macdonald bessel function the phase velocity of on s imz 1 is a double valued vector field the tangent field to the pencil of geodesics g tangent to the horocycle s imz 1 for a sl 2 r a multi term stationary phase expansion is presented in a for az e 2 in rez uniform in parameters an application is made to find an asymptotic relation for the fourier coefficients of a family of automorphic eigenfunctions in particular for automorphic with coefficients an and eigenvalue a it is shown for the special range n 1 2 that a n is o 1 4 e 1 2 2 for a large improving by an order of magnitude for this special range upon the estimate from the general hecke bound o n 1 2 1 4 e 1 2 2 an exposition of the wkb asymptotics of the macdonald bessel functions is presented

linear prediction error method for blind identification of periodically time varying channels blind channel estimation for single input multiple output simo periodically time varying channels is considered using only the second order statistics of the data the time varying channel is assumed to be described by a complex exponential basis expansion model ce bem the linear prediction error method for blind identification of time invariant channels is extended to time varying channels represented by a ce bem sufficient conditions for identifiability are investigated the cyclostationary nature of the received signal is exploited to consistently estimate the time varying correlation function of the data from a single observation record the proposed method requires the knowledge of the active basis functions but not the channel length an upper bound suffices several existing methods require precise knowledge of the channel length equalization of the time varying channel given the estimated channel is investigated computer simulation examples are presented to illustrate the approach and to compare it with two existing approaches

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

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

on a whitening approach to partial channel estimation and blind equalization of fir iir multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when a single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers the basis of the approach is the design of a zero forcing equalizer that whitens the noise free data we allow infinite impulse response iir channels moreover the multichannel transfer function need not be column reduced our approaches also work when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the channel length or model orders need not be known the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data a linear prediction approach is also considered under the above conditions of possibly iir channels common subchannel zeros factors and not necessarily column reduced channels four illustrative simulation examples are provided

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

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

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

blind spatio temporal equalization and impulse response estimation for mimo channels using a godard cost function equalization and estimation of the matrix impulse response function of multiple input multiple output mimo digital communications channels in the absence of any training sequences is considered an iterative godard 1980 cost based approach is considered for spatio temporal equalization and mimo impulse response estimation stationary points of the cost function are investigated with particular attention to the case when finite length equalizers exist sufficient conditions are derived under which all stable local minima correspond to desirable minima the inputs are extracted and cancelled one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed

subspace methods for blind estimation of time varying fir channels novel linear algorithms are proposed in this paper for estimating time varying fir systems without resorting to higher order statistics the proposed methods are applicable to systems where each time varying tap coefficient can be described with respect to time as a linear combination of a finite number of basis functions examples of such channels include almost periodically varying ones fourier series description or channels locally modeled by a truncated taylor series or by a wavelet expansion it is shown that the estimation of the expansion parameters is equivalent to estimating the second order parameters of an unobservable fir single input many output simo process which are directly computed under some assumptions from the observation data by exploiting this equivalence a number of different blind subspace methods are applicable which have been originally developed in the context of time invariant simo systems identifiability issues are investigated and some illustrative simulations are presented

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

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