bmo spaces associated with semigroups of operators we study bmo spaces associated with semigroup of operators on noncommutative function spaces i e von neumann algebras and apply the results to boundedness of fourier multipliers on non abelian discrete groups we prove an interpolation theorem for bmo spaces and prove the boundedness of a class of fourier multipliers on noncommutative lp spaces for all 1 p with optimal constants in p

an operator valued t1 theory for symmetric czos abstract we provide a natural bmo criterion for the l 2 boundedness of calderon zygmund operators with operator valued kernels satisfying a symmetric property our arguments involve both classical and quantum probability theory in the appendix we give a proof of the l 2 boundedness of the commutators r j b whenever b belongs to the bourgain s vector valued bmo space where r j is the j th riesz transform a common ingredient is the operator valued haar multiplier studied by blasco and pott

une minoration de la norme de l operateur de cauchy sur les graphes lipschitziens it was shown by t murai that the norm of the operator defined by the cauchy kernel on the graph of a lipschitz function a is less than c 1 iiatlioo l 2 we use garnett s example to show that this estimate is optimal

use of the viterbi algorithm to compute error events of trellis phase coding in order of increasing distance the use of the viterbi algorithm to evaluate the minimum distance parameters of trellis phase codes is extended to evaluate distances and paths of error events other than the free distance event distances and paths are found for error events sequentially in order of increasing distance starting with the free distance event memory requirements increase slowly with the number of error events required the time taken to find the next error event increases slowly with the number of error events already found results of sample calculations and computation times are included

s numbers of singular integrals for the invariance of absolutely continuous spectra in fractional dimensions an important consequence of the kato rosenblum theorem in abstract scattering theory 5 81 is the invariance up to unitary equivalence of absolutely continuous spectra under trace class perturbations the extension of this fact to higher integral dimensions was given in lo a careful inspection of trace class scattering theory reveals the crucial role of l2 boundedness of the hilbert transform in the one dimensional case in the n dimensional generalization this is replaced by the asymptotics of fourier coefficients of 2 1 x k c n 1 11 2 on the torus or equivalently by the asymptotics of s numbers of corresponding singular integrals the general functional analysis machinery developed in 9 lo for studying normed ideal perturbations of systems of hilbert space operators reduces this kind of operator theory questions to questions about the existence or non existence of quasicentral approximate units relative to normed ideals the existence of quasicentral approximate units in turn is related to commutator questions 11 j for related considerations in the quasidiagonality context see 7 the natural operators to examine are then singular integral operators in this paper we consider the fractional dimensional case the natural singular integral problem in this case is to estimate the s numbers of singular integrals with kernels yjl lx 1 in l p where 1 is a compactly supported probability measure on w of fractional dimension like hausdorff measure restricted to suitable compacta the results we

variation of discrete spectra a formula see 1 below estimating collectively the variation of eigenvalues of a symmetric matrix under a perturbation is extended to the case of discrete eigenvalues of a selfadjoint operator in hilbert space under the assumption that the perturbation is compact for this purpose the notion of an extended enumeration of discrete eigenvalues is introduced

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

a generalization of voiculescu s theorem for normal operators to semifinite von neumann algebras abstract in this paper we provide a generalized version of voiculescu s theorem for normal operators by showing that in a von neumann algebra with separable pre dual and a faithful normal semifinite tracial weight each normal operator is an arbitrarily small max 2 norm perturbation of a diagonal operator furthermore in a countably decomposable properly infinite von neumann algebra with a faithful normal semifinite tracial weight we prove that each self adjoint operator can be diagonalized modulo normed ideals satisfying a natural condition an analogue for nuclear c algebras of voiculescu s absorption theorem 33 theorem 2 4 is also proved in the case of semifinite factors

asymmetric doob inequalities in continuous time abstract the present paper is devoted to the second part of our project on asymmetric maximal inequalities where we consider martingales in continuous time let m be a noncommutative probability space equipped with a continuous filtration of von neumann subalgebras m t 0 t 1 whose union is weak dense in m let e t denote the corresponding family of conditional expectations as for discrete filtrations we shall prove that for 1 p 2 and x l p m one can find a b l p m and contractions u t v t m such that e t x a u t v t b and max a p b p c p x p moreover a u t and v t b converge in the row column hardy spaces h p r m and h p c m respectively we also confirm in the continuous setting the validity of related asymmetric maximal inequalities which we recently found for discrete filtrations including p 1 as for other results in noncommutative martingale theory the passage from discrete to continuous index is quite technical and requires genuinely new methods our approach towards asymmetric maximal inequalities is based on certain construction of conditional expectations for a sequence of projective systems of l p modules the convergence in h p r m and h p c m also imposes new algebraic atomic decompositions

a condition for diagonalization modulo arbitrary norm ideals abstract we give a spectral condition which is sufficient for the simultaneous diagonalization of a commuting tuple of self adjoint operators modulo a given norm ideal for diagonalization modulo certain norm ideals this condition is also necessary while for other norm ideals this condition seems to be close to being necessary moreover this condition is easy to verify in applications

noncommutative maximal ergodic theorems this paper is devoted to the study of various maximal ergodic theorems in noncommutative spaces in particular we prove the noncommutative analogue of the classical dunford schwartz maximal ergodic inequality for positive contractions on and the analogue of stein s maximal inequality for symmetric positive contractions we also obtain the corresponding individual ergodic theorems we apply these results to a family of natural examples which frequently appear in von neumann algebra theory and in quantum probability

diagonalization modulo a class of orlicz ideals abstract we consider a class of norm ideals c g which are non commutative analogues of orlicz spaces and which satisfy a previously introduced condition called qk we give a spectral condition which is necessary and sufficient for a commuting tuple of self adjoint operators a a 1 a n to be simultaneously diagonalizable modulo c g

a new approximation to the symbol error probability for coded modulation schemes with maximum likelihood sequence detection the power efficiency of coded modulation schemes in additive white gaussian noise depends on the signal space distribution of their most common error events symbol error probability calculation allowing for the pairwise interaction of these error events is discussed two optimality criteria are considered for detectors the first minimizes the probability of symbol error for each symbol decision this is called the symbol to symbol detector the second which is superior is the maximum likelihood sequence detector mlsd a lower bound for the symbol to symbol detector and an approximation to the mlsd symbol error probability are described the theoretical performance difference between these two detectors is given the results are more accurate than minimum squared euclidean distance predictions especially at low and intermediate signal to noise ratios the mlsd symbol error probability approximation is obtained for considerably less cost than computer simulation and gives more insight into the signal space structure of the scheme being analyzed numerical results are presented for a continuous phase modulation cpm example

diagonalization modulo norm ideals with lipschitz estimates abstract suppose that x d is a compact metric space and that is a regular borel measure on x let lip x denote the collection of lipschitz functions on x in this paper we investigate the problem of simultaneous diagonalization of the multiplication operators m f f lip x on l 2 x modulo norm ideals of compact operators

symbol error probability bounds for coherently viterbi detected continuous phase modulated signals recently the minimum euclidean distance and bandwidth properties of continuous phase modulated cpm signals have been considered it has also been shown that for rational modulation indexes a state description of these signals is possible and that the viterbi algorithm va can be used for demodulation in this paper the performance analysis of cpm systems is extended to obtain bounds on the symbol error probability when the va is used the calculation of these bounds is based on the transfer function technique which has been generalized from numerical comparisons of the upper and lower bounds it is concluded that the minimum euclidean distance is a good performance measure for a broad class of cpm signals even when the symbol error probability is as large as 10 2

singular integral operators and norm ideals satisfying a quantitative variant of kuroda s condition a norm ideal c is said to satisfy condition qk if there exist constants 0 t 1 and 0 b such that x k c bkt x c for every finite rank operator x and every k n where x k denotes the direct sum of k copies of x let be a regular borel measure whose support is contained in a unit cube q in rn and let kj be the singular integral operator on l2 rn with the kernel function xj yj x y 2 1 j n let qw w w be the usual dyadic decomposition of q i e qw w l is the dyadic partition of q by cubes of the size 2 l 2 l we show that if c satisfies qk and if w w2 w qw w w c where c is the dual of c 0 and w w w is any orthonormal set then k1 kn c this is a very general obstruction result for the problem of simultaneous diagonalization of commuting tuples of self adjoint operators modulo c

non commutative martingale inequalities we prove the analogue of the classical burkholder gundy inequalites for non commutative martingales as applications we give a characterization for an ito clifford integral to be an lp martingale via its integrand and then extend the ito clifford integral theory in l2 developed by barnett streater and wilde to lp for all 1 p we include an appendix on the non commutative analogue of the classical fefferman duality between h1 and bmo

noncommutative riesz transforms a probabilistic approach for 2 p 0 in the classical setting this is certainly satisfied for the maps tt f f 1 t where t is a semigroup of measure preserving maps on a probability space in that case n l then the maps tt act on all noncommutative lp spaces lp n and in particular on the hilbert space l2 l2 n let a be the negative generator i e tt e ta for technical reasons we have to assume that there is a weakly dense algebra a n which lies in the domain of the unbounded operator a i e a a a the algebra a plays the role of smooth functions in the classical setting this assumption might be too restrictive for some classical applications but it is easily verified in the new noncommutative examples for elements x y a we may define the gradient form 2 x y a x y x a y a x y the correct definition of is the one given by sauvageot as a bilinear form with values in l1 again our arguments require stronger assumptions in fact in all our examples we will assume that the tt s are selfadjoint i e ttxy xtty and unital i e tt 1 1 then a is indeed a positive unbounded operator under these circumstances we can formulate p a meyer s problem is it true that x x 2 p c p a 1 2 x p 0 1 holds for all selfadjoint elements x a let us illustrate this question by considering the laplace operator a f f where i 2 x2 i then it is easily verified that

diagonalization and unitary equivalence modulo schatten p classes we give a necessary and sufficient condition for a commuting tuple a a1 an of self adjoint operators to be simultaneously diagonalizable modulo cp 1 p