strong sums of projections in von neumann factors abstract this paper presents necessary and sufficient conditions for a positive bounded operator on a separable hilbert space to be the sum of a finite or infinite collection of projections not necessarily mutually orthogonal with the sum converging in the strong operator topology if the collection is infinite a similar necessary condition is given when the operator and the projections are taken in a type ii von neumann factor and the condition is proven to be also sufficient if the operator is diagonalizable a simpler necessary and sufficient condition is given in the type iii factor case

linear preservers of weak majorization on l1 i when i is an infinite set abstract the necessary and sufficient conditions that a bounded linear map on the banach space l 1 i may be considered as a linear preserver of weak majorization on l 1 i where i is an arbitrary infinite set are given also we prove that the set of all linear preservers of weak majorization is closed under the norm topology

operator valued frames we develop a natural generalization of vector valued frame theory we term operator valued frame theory using operator algebraic methods this extends work of the second author and d han which can be viewed as the mul tiplicity one case and extends to higher multiplicity their dilation approach we prove several results for operator valued frames concerning duality dis jointeness complementarity and composition of operator valued frames and the relationship between the two types of similarity left and right of such frames a key technical tool is the parametrization of parseval operator val ued frames in terms of a class of partial isometries in the hilbert space of the analysis operator we apply these notions to an analysis of multiframe gener ators for the action of a discrete group g on a hilbert space one of the main results of the han larson work was the parametrization of the parseval frame generators in terms of the unitary operators in the von neumann algebra gen erated by the group representation and the resulting norm path connectedness of the set of frame generators due to the connectedness of the group of unitary operators of an arbitrary von neumann algebra in this paper we general ize this multiplicity one result to operator valued frames however both the parameterization and the proof of norm path connectedness turn out to be necessarily more complicated and this is at least in part the rationale for this paper our parameterization involves a class of partial isometries of a different von neumann algebra these partial isometries are not path connected in the norm topology but only in the strong operator topology we prove that the set of operator frame generators is norm pathwise connected precisely when the von neumann algebra generated by the right representation of the group has no minimal projections as in the multiplicity one theory there are analogous results for general non parseval frames

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

on state versus channel quantum extension problems exact results for u otimes u otimes u symmetry we develop a framework which unifies seemingly different extension or joinability problems for bipartite quantum states and channels this includes known extension problems such as optimal quantum cloning and quantum marginal problems as special instances central to our generalization is a variant of the jamiolkowski isomorphism between bipartite states and linear transformations which we term the homocorrelation map in contrast to the better known choi isomorphism which emphasizes the preservation of the positivity constraint use of the jamiolkowski isomorphism allows one to characterize the preservation of the statistical correlations of bipartite states and quantum channels the resulting homocorrelation map thus acquires a natural operational interpretation we define and analyze state joining channel joining and local positive joining problems in three party settings with collective symmetry obtaining exact analytical characterizations in low dimensions we find that bipartite quantum states are limited in the degree to which their measurement outcomes may agree whereas quantum channels are limited in the degree to which their measurement outcomes may disagree loosely speaking quantum mechanics enforces an upper bound on the strength of positive correlation across two subsystems at a single time as well as on the strength of negative correlation between the state of a single system across two instants of time we argue that these general statistical bounds inform the quantum joinability limitations and show that they are in fact sufficient for the three party invariant setting

traces ideals and arithmetic means this article grew out of recent work of dykema figiel weiss and wodzicki commutator structure of operator ideals which inter alia characterizes commutator ideals in terms of arithmetic means in this paper we study ideals that are arithmetically mean am stable am closed am open soft edged and soft complemented we show that many of the ideals in the literature possess such properties we apply these notions to prove that for all the ideals considered the linear codimension of their commutator space the number of traces on the ideal is either 0 1 or we identify the largest ideal which supports a unique nonsingular trace as the intersection of certain lorentz ideals an application to elementary operators is given we study properties of arithmetic mean operations on ideals e g we prove that the am closure of a sum of ideals is the sum of their am closures we obtain cancellation properties for arithmetic means for principal ideals a necessary and sufficient condition for first order cancellations is the regularity of the generator for second order cancellations sufficient conditions are that the generator satisfies the exponential 2 condition or is regular we construct an example where second order cancellation fails thus settling an open question we also consider cancellation properties for inclusions and we find and use lattice properties of ideals associated with the existence of gaps

a schur horn kostant convexity theorem for the diffeomorphism group of the annulus the group of area preserving diffeomorphisms of the annulus acts on its lie algebra the globally hamiltonian vectorfields on the annulus we consider a certain hilbert space completion of this group thinking of it as a group of unitary operators induced by the diffeomorphisms and prove that the projection of an adjoint orbit onto a cartan subalgebra isomorphic tol2 0 1 is an infinite dimensional weakly compact convex set whose extreme points coincide with the orbit through a certain function of the permutation semigroup of measure preserving transformations of 0 1

quasi doubly stochastic operator on l1 and nielsen s theorem in this paper we introduce the quasidoubly stochastic operator which is between doubly stochastic operators and column stochastic operators so as to apply to characterized operator s on l1 such that sf is majorized by f for every f l1 we present some classes of majorization preservers on l1 under quasi doubly stochastic operators moreover as an application of our result in quantum physics the convertibility of pure states of a composite system by local operations and classical communication has been considered

optimal reconstruction systems for erasures and for the q potential abstract in this paper we introduce the q potential as an extension of the benedetto fickus frame potential defined on general reconstruction systems and show that protocols are the minimizers of this potential under certain restrictions we extend recent results of b g bodmann on the structure of optimal protocols with respect to 1 and 2 lost packets where the worst normalized reconstruction error is computed with respect to a compatible unitarily invariant norm we finally describe necessary and sufficient spectral conditions that we call q fundamental inequalities for the existence of protocols with prescribed properties by relating this problem to klyachko s and fulton s theory on sums of hermitian operators

linear preservers of weak majorization on lp i when p 1 abstract we present a necessary and sufficient conditions that a bounded linear map on l p i when p 1 may be considered as a linear preserver of weak majorization on l p i where i is an arbitrary infinite set we also prove that the class of all linear preservers of weak majorization is closed under the norm topology

cusps of the kahler moduli space and stability conditions on k3 surfaces ma int j math 20 6 727 750 2009 established a bijection between fourier mukai partners of a k3 surface and cusps of the kahler moduli space the kahler moduli space can be described as a quotient of bridgeland s stability manifold we study the relation between stability conditions near to a cusp and the associated fourier mukai partner y in the following ways 1 we compare the heart of to the heart of coherent sheaves on y 2 we construct y as moduli space of stable objects an appendix is devoted to the group of auto equivalences of mathcal d b x which respect the component stab dagger x of the stability manifold

on the diagonal of an operator characterlzatlons of zero diagonal operators i e operatcors that have a diagonal whose entries consist entirely of zeros and the ncorm closure of these operators are obtalned also lncluded are new characterlzations of trace class operators self colnmutators of bcounded operatcors and others o introduction in 3 it is shown that a hermitian compact operator is a self commutator of a compact operator if and only if it has a zero diagonal motivated by this result we decided to launch an investigation into the connection between the diagonal of an operator and the operator itself we wonder to what extent an operator can be described by its diagonal it turns out that as expee ted the diagonal of an operator carries more information about the operator than its relatively small size compare to the fat matrix representation of the operator may suggest let h be a complex separable hilbert space and bf h the space of a11 bounded operators on h by zero diagonal operators we mean the operators t such that there exists an orthonormal basis bj for h satisfying tbj hx 0 for all j it is not hard to see that the set of these operators is pathwise connected in fact all its elements can be connected to the origin 0 inside itself that it is not a linear manifold 2i ed i and i d3 21 belong to it but their sum i i does not and moreover that it stays away from i indeed the distance is no less than one take a zero diagonal operator t and choose an orthonormal basis b so that tby b 0 then iit iil supllxlls t i x x t i bl bj 1 in the first section we are to characterize zero diagonal operators and hermitian

isotonic linear operators on the space of all convergent real sequences abstract in this work we consider a natural preorder on c the banach space of all convergent real sequences which is called convex majorization we find a large class of bounded linear operators t c c which preserve convex majorization and denote this class by i then some interesting properties of each t i are obtained

trace class operators and commutators abstract we identify the linear span of commutators ab ba where a is a trace class operator and b is any bounded operator on a separable hilbert space or where a b are both hilbert schmidt operators thus answering questions raised by work of anderson vaserstein and weiss

a contractive version of a schur horn theorem in ii1 factors we prove a contractive version of the schur horn theorem for submajorization in ii1 factors that complements some previous results on the schur horn theorem within this context we obtain a reformulation of a conjecture of arveson and kadison regarding a strong version of the schur horn theorem in ii1 factors in terms of submajorization and contractive orbits of positive operators

extending a characterization of majorization to infinite dimensions abstract we consider recent work linking majorization and trumping two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information with general dirichlet polynomials mellin transforms and completely monotone sequences we extend a basic majorization result to the more physically realistic infinite dimensional setting through the use of generalized dirichlet series and riemann stieltjes integrals

the geometric theta correspondence for hilbert modular surfaces we give a new proof and an extension of the celebrated theorem of hirzebruch and zagier 17 that the generating function for the intersection numbers of the hirzebruch zagier cycles in certain hilbert modular surfaces is a classical modular form of weight 2 in our approach we replace hirzebuch s smooth complex analytic compactification of the hilbert modular surface with the real borel serre compactification the various algebro geometric quantities that occur in 17 are replaced by topological quantities associated to 4 manifolds with boundary in particular the boundary contribution in 17 is replaced by sums of linking numbers of circles the boundaries of the cycles in 3 manifolds of type sol torus bundle over a circle which comprise the borel serre boundary

frames graphs and erasures two uniform frames and their use for the coding of vectors are the main subject of this paper these frames are known to be optimal for handling up to two erasures in the sense that they minimize the largest possible error when up to two frame coefficients are set to zero here we consider various numerical measures for the reconstruction error associated with a frame when an arbitrary number of the frame coefficients of a vector are lost we derive general error bounds for two uniform frames when more than two erasures occur and apply these to concrete examples we show that among the 227 known equivalence classes of two uniform 36 15 frames arising from hadamard matrices there are 5 that give smallest error bounds for up to 8 erasures

pinchings and positive linear maps abstract we employ the pinching theorem ensuring that some operators a admit any sequence of contractions as an operator diagonal of a to deduce improve two recent theorems of kennedy skoufranis and loreaux weiss for conditional expectations onto a masa in the algebra of operators on a hilbert space similarly we obtain a proof of a theorem of akeman and anderson showing that positive contractions in a continuous masa can be lifted to a projection we also discuss a few corollaries for sums of two operators in the same unitary orbit

schur products of operators and the essential numerical range let e en 00 i be an orthonormal basis for a hilbert space 9c for operators a and b having matrices a x and b xo their schur product is defined to be aijbu this gives f 9c a new banach algebra structure denoted 13 for any operator t it is shown that t is in the kernel hull compact operators in some 13 iff 0 is in the essential numerical range of t these conditions are also equivalent to the property that there is a basis such that schur multiplication by t is a compact operator mapping schatten classes into smaller schatten classes thus we provide new results linking f 9c and 1 f 9c let c be a separable infinite dimensional hilbert space and a b be bounded operators on k for an orthonormal basis en 1 n oo of jc a and b have matrix representations aij j 1 and b in 1911 schur 15 p 8 proved that the termwise product a b j 1 denoted a b is itself a bounded operator with norm satisfying ia b isi i a b this multiplication will herein be called schur multiplication as opposed to the more common but falsely crediting hadamard multiplication schur s result shows that once a basis is selected then defines a commutative banach algebra denoted by 5g while there is a surge of interest in applications of schur multiplication see for example bennett 3 johnson and williams 6 pommerenke 11 or styan 18 litle is known about the structure of i f in particular few connections between the structure of b s and i have been explored though varopoulos 20 has asked whether the linear structure of i sc forces to be a q algebra except for bennett 4 and ruckle 13 the systematic study of schur multiplication as a means of obtaining unusual operators in 1 13 j is a relatively untouched concept even though several interesting operators are schur multipliers e g kwapien and pelczynski 8 it is important to keep in mind that a b depends upon a choice of basis the symbol as will be used to denote the element of i xo defined by a b a b where is with respect to the basis 6 it will be shown that the following conditions and several others are equivalent for any operator t i 0 is in the essential numerical range of t ii there exists a basis such that t is in kernel hull fc where 3c is the ideal of compact operators in 613 received by the editors october 19 1979 and in revised form march 3 1980 1980 mathematics subject classification primary 47a12 47d99 secondary 46j99

openness and convexity for momentum maps the purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps it is shown that they are of a topological nature more specifically we show that convexity follows if the map is open onto its image and has the so called local convexity data property these conditions are satisfied in all the classical convexity theorems and hence they can in principle be obtained as corollaries of a more general theorem that has only these two hypotheses we also prove a generalization of the so called local to global principle that only requires the map to be closed and to have a normal topological space as domain instead of using a properness condition this allows us to generalize the flaschka ratiu convexity theorem to noncompact manifolds

optimal frames for erasures we study frames from the viewpoint of coding theory we introduce a numerical measure of how well a frame reconstructs vectors when some of the frame coefficients of a vector are lost and then attempt to find and classify the frames that are optimal in this setting

diagonals of normal operators with finite spectrum let x lambda1 lambdan be a finite set of complex numbers and let a be a normal operator with spectrum x that acts on a separable hilbert space h relative to a fixed orthonormal basis e1 e2 for h a gives rise to a matrix whose diagonal is a sequence d d1 d2 with the property that each of its terms dn belongs to the convex hull of x not all sequences with that property can arise as the diagonal of a normal operator with spectrum x the case where x is a set of real numbers has received a great deal of attention over the years and is reasonably well though incompletely understood in this work we take up the case in which x is the set of vertices of a convex polygon in the critical sequences d turn out to be those that accumulate rapidly in x in the sense that sigmainfinityn 1 dist dn x s d e gammax with the following property if s d not equal 0 then d is not the diagonal of any such operator a we also show that while this is the only obstruction when n 2 there are other as yet unknown obstructions when n 3

majorization on l and on its closed linear subspace c and their linear preservers abstract in this paper we extend the notion of majorization to l the banach space of all bounded real sequences and investigate some of its properties considering this notion on c the subspace of all convergent real sequences the structure of all bounded linear operators which preserve the majorization relation on this subspace is obtained finally we introduce two different classes of linear preservers of majorization on l which illustrate some important differences between the structure of these operators on l and those on l p spaces for 1 p as well as those on c

closed convex hulls of unitary orbits in c algebras of real rank zero abstract in this paper we study closed convex hulls of unitary orbits in various c algebras for unital c algebras with real rank zero and a faithful tracial state determining equivalence of projections a notion of majorization describes the closed convex hulls of unitary orbits for self adjoint operators other notions of majorization are examined in these c algebras combining these ideas with the dixmier property we demonstrate unital infinite dimensional c algebras of real rank zero and strict comparison of projections with respect to a faithful tracial state must be simple and have a unique tracial state also closed convex hulls of unitary orbits of self adjoint operators are fully described in unital simple purely infinite c algebras

the spectral side of arthur s trace formula the trace formula is one of the most important tools in the theory of automorphic forms it was invented in the 1950 s by selberg who mostly studied the case of hyperbolic surfaces and was later on developed extensively by arthur in the generality of an adelic quotient of a reductive group over a number field here we provide an explicit expression for the spectral side improving arthur s fine spectral expansion as a result we obtain its absolute convergence for a wide class of test functions

an infinite dimensional schur horn theorem and majorization theory the main result of this paper is the extension of the schur horn theorem to infinite sequences for two nonincreasing nonsummable sequences and that converge to 0 there exists a positive compact operator a with eigenvalue list and diagonal sequence if and only if j 1n j j 1n j for every n if and only if q for some orthostochastic matrix q when and are summable requiring additionally equality of their infinite series obtains the same conclusion extending a theorem by arveson and kadison our proof depends on the construction and analysis of an infinite product of t transform matrices

multivariable schur horn theorems fil massey pedro gustavo universidad nacional de la plata facultad de ciencias exactas departamento de matematicas argentina consejo nacional de investigaciones cientificas y tecnicas oficina de coordinacion administrativa saavedra 15 instituto argentino de matematica alberto calderon argentina

an infinite dimensional version of the schur horn convexity theorem the schur horn convexity theorem states that forain rnp u diag a u u u n conv sna wherepdenotes the projection on the diagonal in this paper we generalize this result to the setting of arbitrary separable hilbert spaces it turns out that the theorem still holds if we take thel closure on both sides we will also give a description of the left hand side for nondiagonalizable hermitian operators in the last section we use this result to get an extension theorem for invariant closed convex subsets of the diagonal operators

optimal cloning and singlet monogamy the inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins despite this there is no quantitative link between how much entanglement can be generated between spins and how well an unknown state can be cloned this situation is remedied by giving a set of sufficient conditions such that a completely positive map can be optimally implemented as a teleportation operation into a standard reference state the case of arbitrary 1 ensuremath rightarrow n asymmetric cloning of d dimensional spins can then be solved exactly yielding the concept of singlet monogamy the utility of this relation is demonstrated by calculating properties of heisenberg systems and contrasting them with the results from standard monogamy arguments

an extension of wiener integration with the use of operator theory with the use of tensor product of hilbert space and a diagonalization procedure from operator theory we derive an approximation formula for a general class of stochastic integrals further we establish a generalized fourier expansion for these stochastic integrals in our extension we circumvent some of the limitations of the more widely used stochastic integral due to wiener and ito i e stochastic integration with respect to brownian motion finally we discuss the connection between the two approaches as well as a priori estimates and applications

the pythagorean theorem i the finite case the pythagorean theorem and variants of it are studied the variations evolve to a formulation in terms of noncommutative conditional expectations on von neumann algebras that displays the theorem as the basic result of noncommutative metric euclidean geometry the emphasis in the present article is finite dimensionality both discrete and continuous

dilation theory and systems of simultaneous equations in the predual of an operator algebra ii 1 this note is a continuation of our earlier paper 3 in which we developed a dilation theory for a certain class of contraction operators acting on a separable infinite dimensional complex hilbert space the notation and terminology in what follows is taken from 3 for the convenience of the reader we recall a few pertinent definitions the algebra of bounded linear operators on is denoted by y if t se 2c the ultraweakly closed algebra generated by t and l e is denoted by dr we recall that d r can be identified with the dual space of the quotient space q r z c where zc denotes the ideal of trace class operators in 5 24 and is the preannihilator of d r in z c under the pairing

the pythagorean theorem ii the infinite discrete case the study of the pythagorean theorem and variants of it as the basic result of noncommutative metric euclidean geometry is continued the emphasis in the present article is the case of infinite discrete dimensionality

circles in the spectrum and the geometry of orbits a numerical ranges approach abstract we prove that a bounded linear hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost orthogonality relations this result is obtained via the study of numerical ranges of operator tuples where several new results are also obtained as consequences of our numerical ranges approach we derive in particular wide generalizations of arveson s theorem as well as show that the weak convergence of operator powers implies the uniform convergence of their compressions on an infinite dimensional subspace

strong monogamy conjecture for multiqubit entanglement the four qubit case we investigate the distribution of bipartite and multipartite entanglement in multiqubit states in particular we define a set of monogamy inequalities sharpening the conventional coffman kundu wootters constraints and we provide analytical proofs of their validity for relevant classes of states we present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits

entropy encoding hilbert space and karhunen loeve transforms by introducing hilbert space and operators we show how probabilities approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates our main results yield orthogonal bases which optimize distinct measures of data encoding

iwasawa decompositions of some infinite dimensional lie groups we set up an abstract framework that allows the investigation of iwasawa decompositions for involutive infinite dimensional lie groups modeled on banach spaces this provides a method to construct iwasawa decompositions for classical real or complex banach lie groups associated with the schatten ideals o p h on a complex separable hilbert space h if 1 p

von neumann entropy and majorization abstract we consider the properties of the shannon entropy for two probability distributions which stand in the relationship of majorization then we give a generalization of a theorem due to uhlmann extending it to infinite dimensional hilbert spaces finally we show that for any quantum channel one has s s for all quantum states if and only if there exists an isometric operator v such that v v

weak majorization and doubly substochastic operators on lp i abstract we extend the notion of weak majorization on the banach space l p i where i is a non empty set and p 1 using doubly substochastic operators on l p i the close relationship between weak majorization and these operators are presented among others we show that f w g and g w f iff there is a partial permutation p such that g p f using the specific type of positive increasing convex functions a necessary and sufficient condition for f w g and g w f is given

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

commutator structure of operator ideals commutator structure of operator ideals ken dykema 1 tadeusz figiel gary weiss and mariusz wodzicki department of mathematics texas a m university college station tx 77843 3368 usa b instytut matematyczny polskiej akademii nauk 81 825 sopot poland department of mathematical sciences university of cincinnati cincinnati oh 45221 0025 usa department of mathematics university of california berkeley ca 94720 3840 usa

extreme points of the set of elements majorised by an integrable function resolution of a problem by luxemburg and of its noncommutative counterpart abstract let f be an arbitrary integrable function on a finite measure space x we characterise the extreme points of the set f of all measurable functions on x majorised by f providing a complete answer to a problem raised by w a j luxemburg in 1967 moreover we obtain a noncommutative version of this result

the schur horn theorem for operators with three point spectrum abstract we characterize the set of diagonals of the unitary orbit of a self adjoint operator with three points in the spectrum our result gives a schur horn theorem for operators with three point spectrum analogous to kadison s pythagorean theorem and carpenter s theorem which characterize the diagonals of orthogonal projections

weak supermajorization and families as doubly superstochastic operators on lp i abstract we present necessary and sufficient conditions that a family a a i j i j i of real numbers may be considered as a bounded linear operator on banach spaces l 1 i and l i where i is an arbitrary non empty set moreover we get that these conditions are sufficient for a family to be a bounded linear operator on l p i for each p 1 within this class of operators the notion of doubly superstochastic operator is introduced as an extension of the doubly superstochastic matrix and some of its essentially properties are presented in the second part we extend the notion of weak supermajorization relation on the banach space l p i using doubly superstochastic operators and present close relationship between this relation and superstochastic operators as generalisation well known results in the theory of majorization among others for two functions f g l 1 i we show that relations f w s g and g w s f hold if and only if there exist a permutation p such that g p f

frames of translates with prescribed fine structure in shift invariant spaces abstract for a given finitely generated shift invariant fsi subspace w l 2 r k we obtain a simple criterion for the existence of shift generated sg bessel sequences e f induced by finite sequences of vectors f w n that have a prescribed fine structure i e such that the norms of the vectors in f and the spectra of s e f are prescribed in each fiber of spec w t k we complement this result by developing an analogue of the so called sequences of eigensteps from finite frame theory in the context of sg bessel sequences that allows for a detailed description of all sequences with prescribed fine structure then given 1 n 0 we characterize the finite sequences f w n such that f i 2 i for 1 i n and such that the fine spectral structure of the shift generated bessel sequences e f has minimal spread i e we show the existence of optimal sg bessel sequences with prescribed norms in this context the spread of the spectra is measured in terms of the convex potential p w induced by w and an arbitrary convex function r r

generalized monogamy of contextual inequalities from the no disturbance principle in this letter we demonstrate that the property of monogamy of bell violations seen for no signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the gleason property of no disturbance we show how one can construct monogamies for contextual inequalities by using the graph theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution after establishing that all the subgraphs that are chordal graphs admit a joint probability distribution we formulate a precise graph theoretic condition that gives rise to the monogamy of contextuality we also show how such monogamies arise within quantum theory for a single four dimensional system and interpret violation of these relations in terms of a violation of causality these monogamies can be tested with current experimental techniques

the structured singular value for linear input output operators in this paper we employ our lifting method to study the structured singular value applied to input output operators of control systems we moreover give a new criterion which guarantees that the structured singular value equals its upper bound defined by d scalings

linear preservers of majorization on lp i abstract in this paper we use doubly stochastic operators to extend the notion of majorization on l p where i is assumed to be an infinite set and p 1 and then characterize the structure of all bounded linear maps on this space which preserve majorization we will see that the two cases p 1 and p 1 lead to different structures