minimal primal and glimm ideal spaces of group c algebras abstract due to recent work of archbold and others primal and glimm ideals in c algebras have gained considerable attention they turned out to be important in representing a c algebra as a maximal full algebra of cross sections and in the estimation of norms of inner derivations in this paper we determine the topological spaces of minimal primal and of glimm ideals in group c algebras for several classes of locally compact groups including all amenable discrete groups the classical motion groups and certain semi direct products of vector groups with the reals

limit sets and strengths of convergence for sequences in the duals of thread like lie groups we consider a properly converging sequence of non characters in the dual space of a thread like group g n n geq 3 and investigate the limit set and the strength with which the sequence converges to each of its limits we show that if k is a properly convergent sequence of non characters in widehat g n then there is a trade off between the number of limits which are not characters their degrees and the strength of convergence i to each of these limits theorem 3 2 this enables us to describe various possibilities for maximal limit sets consisting entirely of non characters theorem 4 6 in sect 5 we show that if k is a properly converging sequence of non characters in widehat g n and if the limit set contains a character then the intersection of the set of characters which is homeomorphic to mathbb r 2 with the limit set has at most two components in the case of two components each is a half plane in theorem 7 7 we show that if a sequence has a character as a cluster point then by passing to a properly convergent subsequence and then a further subsequence it is possible to find a real null sequence c k with c k ne 0 such that for a in the pedersen ideal of c g n lim k rightarrow infty c k rm tr pi k a exists not identically zero and is given by a sum of integrals over mathbb r 2

conservation laws for equations of mixed elliptic hyperbolic and degenerate types for partial differential equations of mixed elliptic hyperbolic and degenerate types which are the euler lagrange equations for an associated lagrangian invariance with respect to changes in independent and dependent variables is investigated as are results in the classification of continuous one parameter symmetry groups for the variational and divergence symmetries conservation laws are derived via the method of multipliers the conservation laws resulting from anisotropic dilations are applied to prove uniqueness theorems for linear and nonlinear problems and the invariance under dilations of the linear part is used to derive critical exponent phenomena and to obtain localized energy estimates for supercritical problems

purely infinite simple c algebras that are principal groupoid c algebras abstract from a suitable groupoid g we show how to construct an amenable principal groupoid whose c algebra is a kirchberg algebra which is kk equivalent to c g using this construction we show by example that many uct kirchberg algebras can be realised as the c algebras of amenable principal groupoids

on the behaviour of sequences in the dual of a nilpotent lie group let a be a separable c algebra and let c he a subset of the dual space 4 of a denote by a the cone of the positive elements in a we say that x e a is an element with bounded trace on c if the function n tr it x is bounded on c put bt xea x with bounded trace on 7 and let btc be the two sided selfadjoint ideal in a generated by bt let us set hc for the hull of btc in 4 i e

the linearized system for isometric embeddings and its characteristic variety abstract in this paper we prove a conjecture of bryant griffiths and yang concerning the characteristic variety for the determined isometric embedding system in particular we show that the characteristic variety is not smooth for any dimension greater than 4 this is accomplished by introducing a smaller yet equivalent linearized system in an appropriate way which facilitates analysis of the characteristic variety

solvable lie algebras of dimension six six dimensional solvable lie algebras over the field of real numbers that possess nilradicals of dimension four are classified into equivalence classes this completes mubarakzyanov s classification of the real six dimensional solvable lie algebras

the mackey glimm dichotomy for foliations and other polish groupoids abstract for polish groups acting on polish spaces e effros gave a condition under which 14 properties of the orbits or the orbit space of an anti ergodic character are equivalent he also raised the question of extending these results to polish groupoids and this paper gives an affirmative answer to that question the paper also includes results about totally disconnected quotient spaces and an application to indecomposable continua

extensions of pure states and projections of norm one abstract we show that the extension property for pure states of a c subalgebra b of a c algebra a leads to the existence of a projection of norm one r a b in the case where b is liminal with hausdorff primitive ideal space furthermore r is given by a dixmier process in which the averaging is effected by a group of unitary elements in the centre of the multiplier algebra m b these results generalize earlier work of j anderson and the author for the case when b is a masa of a various applications are given in the context of inductive limit algebras such as af algebras and more generally kumjian s ultraliminary c algebras

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

restricted p isometry properties of nonconvex matrix recovery recently a nonconvex relaxation of low rank matrix recovery lmr called the schatten p quasi norm minimization 0 p 1 was introduced instead of the previous nuclear norm minimization in order to approximate the problem of lmr closer in this paper we introduce a notion of the restricted p isometry constants 0 p 1 and derive a p rip condition for exact reconstruction of lmr via schatten p quasi norm minimization in particular we determine how many random gaussian measurements are needed for the p rip condition to hold with high probability which gives a theoretical result that it needs fewer measurements with small p for exact recovery via schatten p quasi norm minimization than when p 1

global bv entropy solutions to the gauss codazzi system abstract the gauss codazzi system for the given metric whose gauss curvature is negative is considered in the present paper we provide some suitable conditions on the given metric such that the system admits a global bv entropy solution our main approach is applying the method of seeking global bv entropy solutions to the hyperbolic system of balance laws to the gauss codazzi system the global existence of bv solutions to the gauss codazzi system yields a c 1 1 isometric immersion of two dimensional manifold into r 3

the local isometric embedding in r3 of two dimensional riemannian manifolds with gaussian curvature changing sign cleanly on etudie le plongement isometrique local de surfaces a 2 dimensions dans r 3 on suppose que la premiere forme fondamentale edu 2 2fdudv gdv 2 on cherche trois fonctions c 2 x u v y u v z u v telles que dx 2 dy 2 dz 2 edu 2 2fdudv gdv 2 dans un voisinage de p

dirichlet problems for general monge ampere equations here 172z denotes the hessian of z with respect to a given metric d s2 gu d u d u a in the local chart vzz z u f z where are the christoffel symbols there have been many papers to devoted to the boundary value problems of 1 1 for example cns1 2 t k tu h1 and most of them are only concerning the euclidean metric the purpose of the present paper is to deal with the dirichlet problem of 1 1 for any given metric as a moderate step in sect 2 and 3 we discuss the following problem

on group algebras of bounded representation dimension we consider the structure of group c algebras whose irreducible representations have bounded dimension we give some general results including a description of the topology on the spectrum and then calculate explicitly the c algebras of two specific groups one of them a nonsymmorphic space group

characterization of the subdifferential of some matrix norms abstract a characterization is given of the subdifferential of matrix norms from two classes orthogonally invariant norms and operator or subordinate norms specific results are derived for some special cases

boundary value problems for mixed type equations and applications abstract in this paper we outline a general method for finding well posed boundary value problems for linear equations of mixed elliptic and hyperbolic type which extends previous techniques of berezanskii didenko and friedrichs this method is then used to study a particular class of fully nonlinear mixed type equations which arise in applications to differential geometry

existence of c local solutions for the monge ampere equation on considere l equation de monge ampere det u ij f y u u dans un ouvert de r n on demontre l existence de solutions c locales

bv weak solutions to gauss codazzi system for isometric immersions abstract the isometric immersion problem for surfaces embedded into r 3 is studied via the fluid dynamic framework introduced in chen et al 2010 6 as a system of balance laws of mixed type the techniques developed in the theory of weak solutions of bounded variation in continuum physics are employed to deal with the isometric immersions in the setting of differential geometry the so called bv framework is formed that establishes convergence of approximate solutions of bounded variation to the gauss codazzi system and yields the c 1 1 isometric realization of two dimensional surfaces into r 3 local and global existence results are established for weak solutions of small bounded variation to the gauss codazzi system for negatively curved surfaces that admit equilibrium configurations as an application the case of catenoidal shell of revolution is provided

bounded trace c algebras and integrable actions let g be a second countable group a be a separable c algebra with bounded trace and a strongly continuous action of g on a suppose that the action of g on open image in new window induced by is free and the g orbits are locally closed we show that the crossed product a g has bounded trace if and only if g acts integrably in the sense of rieffel and an huef on open image in new window in the course of this we show that the extent of non properness of an integrable action gives rise to a lower bound for the size of the finite upper multiplicities of the irreducible representations of the crossed product

necessary and sufficient null space condition for nuclear norm minimization in low rank matrix recovery low rank matrix recovery has found many applications in science and engineering such as machine learning system identification and euclidean embedding however the low rank matrix recovery problem is an np hard problem and thus challenging a commonly used heuristic approach is the nuclear norm minimization recently some authors established the necessary and sufficient null space conditions for nuclear norm minimization to recover every possible low rank matrix with rank at most r the strong null space condition oymak et al established a null space condition for successful recovery of a given low rank matrix the weak null space condition using nuclear norm minimization and derived the phase transition for the nuclear norm minimization in this paper we show that the weak null space condition proposed by oymak et al is only a sufficient condition for successful matrix recovery using nuclear norm minimization and is not a necessary condition as claimed we further give a weak null space condition for low rank matrix recovery which is both necessary and sufficient for the success of nuclear norm minimization at the core of our derivation are an inequality for characterizing the nuclear norms of block matrices and the conditions for equality to hold in that inequality

existence of distributional solutions of a closed dirichlet problem for an elliptic hyperbolic equation abstract the closed dirichlet problem for an elliptic hyperbolic equation arising in linearizing the monge ampere type equation is shown to admit a distributional solution by using an a b c integral method

upper multiplicity and bounded trace ideals inc algebras upper and lower multiplicitiesmu andml for an irreducible representation of ac algebraa relative to a net in are shown to generalize the multiplicity numbers obtained by previous authors in trace formulae for group c algebras this leads in the presence of an auxiliary finiteness condition to anuppersemi continuity result in 0 for trace functions on limsuptr a mu tr a a a where the summation is taken over the cluster points of a characterization is given for the conditionmu k wherekis a positive integer from which it follows that ac algebra has all upper multiplicities finite if and only if it has bounded trace more generally the largest bounded trace idealjof ac algebraais given by mu

a reweighted nuclear norm minimization algorithm for low rank matrix recovery in this paper we propose a reweighted nuclear norm minimization algorithm based on the weighted fixed point method rnnm wfp algorithm to recover a low rank matrix which iteratively solves an unconstrained l 2 m p minimization problem introduced as a nonconvex smooth approximation of the low rank matrix minimization problem we prove that any accumulation point of the sequence generated by the rnnm wfp algorithm is a stationary point of the l 2 m p minimization problem numerical experiments on randomly generated matrix completion problems indicate that the proposed algorithm has better recoverability compared to existing iteratively reweighted algorithms

on the cauchy problem of degenerate hyperbolic equations in this paper we study a class of degenerate hyperbolic equations and prove the existence of smooth solutions for cauchy problems the existence result is based on a priori estimates of sobolev norms of solutions such estimates illustrate a loss of derivatives because of the degeneracy

isometric immersions and compensated compactness a fundamental problem in differential geometry is to characterize intrinsic metrics on a two dimensional riemannian manifold mathcal m 2 which can be realized as isometric immersions into mathbb r 3 this problem can be formulated as initial and or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic hyperbolic type whose mathematical theory is largely incomplete in this paper we develop a general approach which combines a fluid dynamic formulation of balance laws for the gauss codazzi system with a compensated compactness framework to deal with the initial and or boundary value problems for isometric immersions in mathbb r 3 the compensated compactness framework formed here is a natural formulation to ensure the weak continuity of the gauss codazzi system for approximate solutions which yields the isometric realization of two dimensional surfaces in mathbb r 3

improved iteratively reweighted least squares for unconstrained smoothed ell_q minimization in this paper we first study ell q minimization and its associated iterative reweighted algorithm for recovering sparse vectors unlike most existing work we focus on unconstrained ell q minimization for which we show a few advantages on noisy measurements and or approximately sparse vectors inspired by the results in daubechies et al comm pure appl math 63 2010 pp 1 38 for constrained ell q minimization we start with a preliminary yet novel analysis for unconstrained ell q minimization which includes convergence error bound and local convergence behavior then the algorithm and analysis are extended to the recovery of low rank matrices the algorithms for both vector and matrix recovery have been compared to some state of the art algorithms and show superior performance on recovering sparse vectors and low rank matrices

on the central haagerup tensor product and completely bounded mappings of a c algebra we consider the natural contractive map from the central haagerup tensor product of a unital c algebra a with itself to the space of completely bounded maps cb a on a we establish the necessity of the known sufficient condition for isometry of the map namely that all glimm ideals of a are primal however when the map is restricted to tensors with length bounded by a fixed quantity a weaker necessary and sufficient condition is established

elementary operators on hilbert modules over prime c algebras abstract let x be a right hilbert module over a c algebra a equipped with the canonical operator space structure we define an elementary operator on x as a map x x for which there exists a finite number of elements u i in the c algebra b x of adjointable operators on x and v i in the multiplier algebra m a of a such that x i u i x v i for x x if x a this notion agrees with the standard notion of an elementary operator on a in this paper we extend mathieu s theorem for elementary operators on prime c algebras by showing that the completely bounded norm of each elementary operator on a non zero hilbert a module x agrees with the haagerup norm of its corresponding tensor in b x m a if and only if a is a prime c algebra

strength of convergence in the orbit space of a transformation group abstract let g x be a second countable transformation group with g acting freely on x it is shown that measure theoretic accumulation of the action and topological strength of convergence in the orbit space x g provide equivalent ways of quantifying the extent of nonproperness of the action these notions are linked via the representation theory of the transformation group c algebra c 0 x g

strength of convergence in duals of c algebras and nilpotent lie groups abstract by using trace formulae the recent concept of upper multiplicity for an irreducible representation of a c algebra is linked to the earlier notion of strength of convergence in the dual of a nilpotent lie group g in particular it is shown that if has finite upper multiplicity then this integer is the greatest strength with which a sequence in can converge to upper multiplicities are calculated for all irreducible representations of the groups in the threadlike generalization of the heisenberg group the values are computed by combining new c theoretic results with detailed analysis of the convergence of coadjoint orbits and they show that every positive integer occurs for this class of groups

energy estimates for a class of degenerate hyperbolic equations we derive estimates in usual sobolev norms for solutions of degenerate hyperbolic equations if degenerate coefficients admit only real roots loss of derivatives occurs due to the degeneracy

harmonic fields on the extended projective disk and a problem in optics the hodge equations for 1 forms are studied on beltrami s projective disk model for hyperbolic space ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments an existence theorem for weakly harmonic 1 fields changing type on the unit circle is derived under dirichlet conditions imposed on the noncharacteristic portion of the boundary a similar system arises in the analysis of wave motion near a caustic a class of elliptic hyperbolic boundary value problems is formulated for those equations as well for both classes of boundary value problems an arbitrarily small lower order perturbation of the equations is shown to yield solutions which are strong in the sense of friedrichs

convergence of proximal iteratively reweighted nuclear norm algorithm for image processing the nonsmooth and nonconvex regularization has many applications in imaging science and machine learning research due to its excellent recovery performance a proximal iteratively reweighted nuclear norm algorithm has been proposed for the nonsmooth and nonconvex matrix minimizations in this paper we aim to investigate the convergence of the algorithm with the kurdyka ojasiewicz property we prove the algorithm globally converges to a critical point of the objective function the numerical results presented in this paper coincide with our theoretical findings

the c algebras of the heisenberg group and of thread like lie groups we describe the c algebras of the heisenberg group h n n 1 and the thread like lie groups g n n 3 in terms of c algebras of operator fields

lower multiplicity for irreducible representations of nilpotent locally compact groups let g be a nilpotent locally compact group the lower multiplicity ml is defined for every irreducible representation of g which does not form an open point in the dual space of g it is shown that ml 1 if either g is connected or is finite dimensional conversely for g a nilpotent group with small invariant neighbourhoods ml implies that is finite dimensional

completely bounded mappings and simplicial complex structure in the primitive ideal space of a c algebra we consider the natural contraction from the central haagerup tensor product of a c algebra a with itself to the space of completely bounded maps cb a on a and investigate those a where there exists an inverse map with finite norm l a we show that a stabilised version l a sup n l m n a depends only on the primitive ideal space prim a the dependence is via simplicial complex structures defined from primal intersections on finite sets of primitive ideals that contain a glimm ideal of a moreover l a l a k h with k h the compact operators which requires us to develop the theory in the context of c algebras that are not necessarily unital

low tucker rank tensor recovery via admm based on exact and inexact iteratively reweighted algorithms abstract in this paper we establish a non convex l p norm relaxation model for low tucker rank tensor recovery problem and equivalently transform it to a non convex minimization problem with separable structure by introducing series of auxiliary variables in particular we propose two alternating direction method of multipliers admm based on exact and inexact iteratively reweighted algorithms to solve the obtained non convex relaxation problem respectively which are proved to be convergent we implement the proposed algorithms in numerical experiments for solving low tucker rank tensor recovery problem on simulation data and real data and compare them with other existing state of art algorithms numerical results show the effectiveness of the proposed algorithms for solving low rank tensor recovery problem and image recovery

the c algebra of ax b like groups abstract we describe the c algebras of a x b like groups in terms of algebras of operator fields defined over their dual spaces

on the hilbert schmidt semi norms ofl 1 of a nilpotent lie group in 2 appears the convolution product o f f with f on the non abelian group g combined with the abelian fourier transform on r a consequence of this mixture of non abelian with abelian operations is the fact that the integrand f f o exp need not be nonnegative this prohibits the extension of 2 to general ll functions it makes it also difficult to give estimations of ih f la s in terms o f i 7 it would be much better if one could replace 2 by

the central haagerup tensor product and maps between von neumann algebras abstract we introduce the central haagerup tensor product r f h r for a von neumann algebra r and we show that the natural injection into tbe space cb r r of completely bounded maps on r is isometric this is used to study mappings between von neumann algebras and to give a new characterization of injectivity this tensor product is also studied for c algebras a and we show that the injection into cb a a need not always be isometric depending on the topology of the primitive ideal space of a

strength of convergence in non free transformation groups let g x be a transformation group where the group g does not necessarily act freely on the space x we investigate the extent to which the action of g may fail to be proper stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits by using the representation theory of the associated crossed product c algebra we show that these notions are equivalent under certain conditions

strength of convergence in the orbit space of a groupoid abstract let g be a second countable locally compact hausdorff groupoid with a haar system and let x n be a sequence in the unit space g 0 of g we show that the notions of strength of convergence of x n in the orbit space g 0 g and measure theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid c algebra

continuous trace groupoid c algebras iii suppose that g is a second countable locally compact groupoid with a haar system and with abelian isotropy we show that the groupoid c algebra c g has continuous trace if and only if there is a haar system for the isotropy groupoid a and the action of the quotient groupoid g a is proper on the unit space of g

the solvable lie group n_ 6 28 an example of an almost c_0 mathcal k c algebra abstract motivated by the description of the c algebra of the affine automorphism group n 6 28 of the siegel upper half plane of degree 2 as an algebra of operator fields defined over the unitary dual n 6 28 of the group we introduce a family of c algebras which we call almost c 0 k and we show that the c algebra of the group n 6 28 belongs to this class

compactness of alexandrov nirenberg surfaces we study a class of compact surfaces in 3 introduced by alexandrov and generalized by nirenberg and prove a compactness result under suitable assumptions on induced metrics and gauss curvatures 2017 wiley periodicals inc

the local isometric embedding in mathbb r 3 of two dimensional riemannian manifolds with gaussian curvature changing sign to finite order on a curve we consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of monge ampere type these two problems are the local isometric embedding problem for two dimensional riemannian manifolds and the problem of locally prescribed gaussian curvature for surfaces in r3 we prove a general local existence result for a large class of monge ampere equations in the plane and obtain as corollaries the existence of regular solutions to both problems in the case that the gaussian curvature vanishes to arbitrary finite order on a single smooth curve

on the existence of c 1 1 isometric immersions of several classes of negatively curved surfaces into mathbb r 3 we prove the existence of c 1 1 isometric immersions of several classes of negatively curved riemannian surfaces mathcal m g into the 3 dimensional euclidean space mathbb r 3 including the standard hyperbolic plane the generalised helicoid type metrics and the generalised enneper metrics our proof is based on the theory of compensated compactness and the method of invariant regions in hyperbolic conservation laws together with several new observations on relevant geometric quantities gauss curvature metric components etc for negatively curved surfaces

local smooth isometric embeddings of low dimensional riemannian manifolds into euclidean spaces on demontre l existence d un plongement isometrique lisse locale d une 3 variete de riemann lisse a courbure qui ne s annule pas dans un 6 espace euclidien

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

on factorial states of operator algebras results for the factorial state space of a c algebra a which are analogous to results of glimm ann of math 72 1960 216 244 73 1961 572 612 tomiyama and takesaki tohoku math j 2 13 1961 498 523 for the pure state space it is shown that a is prime if and only if the type i factorial states are dense in the state space it follows that every factorial state is a w limit of type i factorial states the factorial state space of a von neumann algebra is determined and it is shown that if a is unital and acts non degenerately on a hilbert space then the factorial state space of the generated von neumann algebra restricts precisely to the factorial state space of a it is shown that the set of factorial states is w compact if and only if a is unital liminal and has hausdorff primitive ideal space

majorized proximal alternating imputation for regularized rank constrained matrix completion abstract low rank approximation in the presence of missing data is ubiquitous in many areas of science and engineering as an np hard problem spectral regularization e g nuclear norm schatten p norm is widely used however solving this problem directly can be computationally expensive due to the unknown rank of variables and full rank singular value decompositions svd bilinear factorization is efficient and effectively benefits from the fast numerical optimization however most of existing methods require explicit knowledge of the rank and often tend to be flatlining or over fitting to balance and take advantage of both we formulate the matrix completion problem under the regularized rank constrained conditions we relax this problem to the surrogates with majorization minimization mm by employing a proximal alternating minimization method to optimize the corresponding surrogates we propose an efficient and accurate algorithm named majorized proximal alternating imputation mpa impute algorithm the proposed method iteratively replaces the missing data at each step with the most recent estimate and only involves simple matrix computation and small scale svd theoretically the proposed method is guaranteed to converge to the stationary point under mild conditions moreover the proposed method can be generalized to a family of non convex regularization problems extensive experiments over synthetic data and real world dataset demonstrate the superior performance of our method