idempotents in nest algebras abstract the algebraic equivalence and similarity classes of idempotents within a nest algebra alg are completely characterized we obtain necessary and sufficient conditions for two idempotents to be equivalent or similar our criterion yields examples illustrating pathology and also shows that to each equivalence class of idempotents there corresponds a dimension function from into n we complete the characterization of the algebraic equivalence classes by proving that any dimension function corresponds to an equivalence class of idempotents also to each sequence of dimension functions there corresponds a commuting sequence of idempotents a criterion is obtained for when an idempotent is similar to a subidempotent of another the mapping which sends an equivalence class or idempotent to its associated dimension function plays a role in the nest algebra theory analogous to the role played by the mapping sending a projection in a type i w algebra to its center valued trace we prove that almost commuting similar idempotents are homotopic this contrasts with the situation in certain c algebras using this we show that similar simultaneously diagonalizable idempotents are homotopic and in the continuous nest case every diagonal idempotent is homotopic to a core projection

coordinates for triangular operator algebras on demontre un theoreme de structure pour des algebres sous diagonales contenant une sous algebre de cartan on etudie les isomorphismes pour ces algebres

on blind identifiability of multipath channels using fractional sampling and second order cyclostationary statistics the problem of blind identifiability of digital communication multipath channels using fractionally spaced samples is considered fractionally sampled data are cyclostationary rather than stationary the problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input information sequence and multiple outputs by using a time series representation of a cyclostationary process a necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process is derived this result provides an alternative but equivalent statement of an existing result using this result it is shown that certain class of multipath channels cannot be identified from the second order statistics irrespective of how the sampling rate is chosen

bisimulation indexes and their applications bisimulation expresses the equivalence of processes whose external actions are identical sometimes we may meet two processes which are not exactly bisimilar but more or less bisimilar in the sense that whenever a process makes an action the other can make an action different from but very similar to the action performed by the first one to describe this kind of looser bisimulations we propose the concept of bisimulation index in a labelled transition system and give its various properties especially those properties related to the operations of transition systems furthermore we establish a modal logical characterization of bisimulation indexes this characterization is a generalization of hennessy milner logic we study strong and weak bisimulation indexes in the basic asynchronous process calculus and some of their fundamental properties are derived bisimulation indexes are not substitutive under composition to overcome this defect we introduce an approximate communication rule to replace the original rule in process calculus this enables us to recover some useful properties of composition with respect to bisimulation indexes finally we present three examples in timed ccs and real time acp to demonstrate the usage of bisimulation indexes in the analysis of real time systems these examples show that bisimulation indexes are suitable formal tools for describing approximate implementations of real time systems

an analogue of a hardy littlewood fejer inequality for upper triangular trace class operators let h denote a separable infinite dimensional hilbert space we shall consider operators that is bounded linear transformations on an operator t is said to be in the schatten class cp if t is compact and if the eigenvalues of t t t 2 are in 1 p 0 p oo the norm in cp is the i p norm of these eigenvalues the class c 2 is called the hilbert schmidt class and c 1 is called the trace class by c o we denote the class of all compact operators for information on these classes see for example 23 4 chap xi 8 chap iii 19 13 although there is an obvious analogy with the sequence spaces i p there is a deeper analogy with the function spaces l p on the unit circle however the containment relations are reversed from the l p case namely cp c cr for p r this analogy serves as a source for new conjectures in operator theory motivated by this we establish an operator analgue of a coefficient inequality for the function space h 1 first we survey some known results in order to emphasize the nature and depth of the analogy fix an orthonormal basis en n l 2 in h and let en span e i en each operator t on has a matrix representation

factorization in analytic operator algebras abstract a constructive and unified approach is used to obtain the upper lower factorization of positive operators and the outer function factorization of positive operator valued functions on the circle for a projection nest e it is shown that every positive operator admits a canonical factorization c a a with a an outer operator if and only if e is well ordered with new methods we generalize the inner outer factorizations obtained by arveson for nests of order type z and the riesz factorization due to shields for trace class triangular operators weak factorization is obtained in noncommutative h1 spaces associated with general nest subalgebras of a semifinite factor characterizations of a nehari type are given for the associated hankel forms and hankel operators

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

mean square stabilizability via output feedback for a non minimum phase networked feedback system this work studies mean square stabilizability via output feedback for a networked linear time invariant lti feedback system with a non minimum phase plant in the feedback system the control signals are transmitted to the plant over a set of parallel communication channels with possible packet dropout our goal is to analytically describe intrinsic constraints among channel packet dropout probabilities and the plant s characteristics in the mean square stabilizability of the system it turns out that this is a very hard problem here we focus on the case in which the plant has relative degree one and each non minimum zero of the plant is only associated with one of control input channels then the admissible region of packet dropout probabilities in the mean square stabilizability of the system is obtained moreover a set of hyper rectangles in this region is presented in terms of the plant s non minimum phase zeros unstable poles and wonham decomposition forms which is related to the structure of controllable subspace of the plant a numerical example is presented to illustrate the fundamental constraints in the mean square stabilizability of the networked system

additive models of probabilistic processes we propose a new model of probabilistic processes in this model a probability is assigned to the action of a prefix and a probability distribution is assigned to the components of a parallel composition in addition the probability of a transition of a probabilistic summation is evaluated as the sum of the probabilities of the same transition of summands multiplied by the probabilities associated to them in the summation the concepts of strong bisimulation degree and weak bisimulation degree are introduced these notions provide us with continuous spectra of strong bisimilarities weak bisimilarities and observation congruences which equate probabilistic processes with different degrees of belief various equational laws of probabilistic processes with respect to these equivalence relations are presented and substitutivities of these equivalence relations under various combinators are established

subdiagonal algebras with beurling type invariant subspaces abstract let a be a maximal subdiagonal algebra in a finite von neumann algebra m if every right invariant subspace of a in the noncommutative hardy space h 2 is of beurling type then we say a is of type 1 we determine generators of these algebras and consider a riesz type factorization theorem for the noncommutative h 1 space we show that the right analytic toeplitz algebra on the noncommutative hardy space h p associated with a type 1 subdiagonal algebra with multiplicity 1 is hereditary reflexive

a shorter proof to uniqueness of solutions of equations we give a very short proof of uniqueness of solutions of equations regarding observation congruence the main notion of equality over milner s process calculus

geometric representation theory for unitary groups of operator algebras geometric realizations for the restrictions of gns representations to unitary groups of c algebras are constructed these geometric realizations use an appropriate concept of reproducing kernels on vector bundles to build such realizations in spaces of holomorphic sections a class of complex coadjoint orbits of the corresponding real banach lie groups are described and some homogeneous holomorphic hermitian vector bundles that are naturally associated with the coadjoint orbits are constructed

the russo dye theorem in nest subalgebras of factors abstract let n be a nest in a factor r in this paper we introduce the concept of the admissible nest for r and prove that the weak operator topology closure of the convex hull of all the unitary elements in the nest subalgebra of the factor is the unit ball if and only if n is an admissible nest in r

characterize branching distance in terms of η α bisimilarity in order to describe approximate equivalence between processes the notion of branching distance has been introduced in the framework of quantitative transition systems this paper introduces the notion of h a bisimilarity and explores the relationship between it and the branching distance

perturbation theory for groups and lattices abstract a generalization of a theorem of dan voiculescu on perturbations of separable c algebras is proved this is applied to solve two problems relating to the perturbation theory of unitary group representations and of commutative subspace lattices the latter generalizes a theorem of niels toft andersen on compact perturbations of nests

invariant subspaces for algebras of analytic operators associated with a periodic flow on a finite von neumann algebra soit m une algebre de von neumann avec un etat et t t est une representation faiblement continue du cercle unite des automorphismes de m tel que t t soit h l ensemble de tous les x m tels que sp x n z n 0 on etudie les sous espaces invariants de h

norm principal bimodules of nest algebras abstract let n be a complete nest in a separable hilbert space h and let alg n be the nest algebra related to n we obtain necessary and sufficient conditions for b h to be principally generated as a norm closed bimodule of alg n the same conditions characterize when b h is principally generated as a norm closed bimodule of the quasitriangular algebra alg n k and when the calkin algebra is principally generated as a norm closed bimodule of the image of alg n under the calkin homomorphism in each case countable generation is equivalent to principal generation

factorization in subdiagonal algebras let m be a finite von neumann algebra and let a be a maximal subdiagonal algebra of m with respect to a faithful normal conditional expectation we show that ifsis an invertible operator in m then there exists an isometrywin m such that boths 1wandw sbelong to a we also give several characterizations of a maximal subdiagonal algebra a such that every invertible operatorsin m can be factored asua whereuis a unitary operator inmand bothaanda 1are in a

noncommutative hardy space associated with semi finite subdiagonal algebras abstract let m be a von neumann algebra with a faithful normal semi finite trace and let a be maximal subdiagonal algebra of m then for 0 p we define the noncommutative h p space we obtain that the conjugation and herglotz maps are bounded linear maps from l p m into l p m for 1 p and continuous map from l 1 m into l 1 m we also give the dual space of h p a for 1 p and extend pisier s interpolation theorem to this case

a process algebra for timed systems a standard process algebra is extended by a new action which is meant to denote idling until the next clock cycle a semantic theory based on testing is developed for the new language this is characterised in terms of barbs a variety of ready traces and also characterised as the initial theory generated by a set of equations

lie isomorphisms of nest algebras abstract in this paper we characterize linear maps between two nest algebras t n and t m which satisfy the property that ab ba a b b a for all a b t n in particular it is shown that such isomorphisms only exist if n is similar to m or m

quasitriangular subalgebras of semifinite von neumann algebras are closed arveson has shown in 1 that if a is a nest algebra of operators acting on a separable hilbert space h with nest of order type the extended natural numbers and if k h is the ideal of compact operators on h then the quasitriangular algebra a k h is norm closed in 6 fall arveson and muhly extended arveson s result proving that in b h general quasitriangular algebras i e compact perturbations of nest algebras are always norm closed a key step in their proof and a result of independent interest first obtained by erdos in s is the a weak density of a n k h in a from this fact they deduced that quasitriangular algebras were norm closed by using an argument depending on the duality k h b h every semifinite von neumann algebra m has an ideal of compact operators that behaves like k h namely the norm closed two sided ideal k generated by the finite projections of the algebra it is a natural question

reliability of mobile processes with noisy channels to model the behavior of channels in real world mobile systems ying introduced an extension of the calculus by taking channel noise into account unfortunately this extension is not faithful in the sense that its semantics does not coincide with the standard one for the calculus in the noise free case in this paper we consider a simple variant of the calculus the asynchronous calculus a which has been used for modeling some concurrent systems with asynchronous communication to model these systems with noisy channels we propose a faithful extension of a called the a n calculus after giving a probabilistic transitional semantics of a n we introduce bisimilarity in a n and show that it is a partial input congruence if a specification of a system is described as a process p in a and we view the behavior of p in a n as an implementation of the specification then it is interesting to measure how far the behavior in a n is from that in a we thus introduce the notion of reliability degree which is based upon a new approximate bisimulation we find that bisimilar agents may have different reliability degrees and even the agent with the greatest reliability degree may not be satisfactory we thus appeal to shannon s noisy channel coding theorem and show that reliability degrees can be improved by employing coding techniques

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

nonminimum phase fir channel estimation using cumulant matrix pencils this paper studies the blind estimation of single input single output channels with finite impulse response fir and nonminimum phase based on higher order statistics we introduce a new algorithm that exploits a matrix pencil constructed from a set of cumulant matrices by solving a generalized eigenvalue problem channel estimates up to a scalar ambiguity can be obtained from nontrivial generalized eigenvectors of this cumulant matrix pencil with multiple estimation results available different schemes are given to extract channel information effectively the proposed algorithm does not require exact knowledge of the channel length and can function properly under channel length overestimation numerical simulations demonstrate the robustness of this new algorithm to various adverse conditions

logmodularity and isometries of operator algebras we generalize some facts about function algebras to operator algebras using the noncommutative shilov boundary or c envelope first considered by arveson in the first part we study and characterize complete isometries between operator algebras in the second part we introduce and study a notion of logmodularity for operator algebras we also give a result on conditional expectations many miscellaneous applications are provided

nest subalgebras of von neumann algebras abstract the structure of a certain class of separably acting reflexive operator algebras is investigated for which the nest algebras of j ringrose can be considered prototypes to a fixed von neumann algebra and a complete nest of projections contained therein one associates the algebra of all operators in the von neumann algebra which leave every member of the nest invariant a generalization of the ringrose criterion for inclusion in the jacobson radical of a nest algebra is given for this more general class of algebras further properties of the radical are studied

mean square small gain theorem for stochastic control discrete time case this paper presents a small gain theorem in the mean square sense for multiple interconnected linear systems with multiplicative noises the small gain theorem is proposed in terms of the spectral radius of a matrix whose elements are the squares of h sub 2 norms of the involved transfer functions both robust stability and performance conditions are characterized by the new small gain theorem

a behavioral distance for fuzzy transition systems in contrast with the existing approaches to exact bisimulation for fuzzy systems we introduce a robust notion of behavioral distance to measure the behavioral similarity of nondeterministic fuzzy transition systems which are a generalization of fuzzy automata this behavioral distance provides a quantitative analogue of bisimilarity and is defined as the greatest fixed point of a suitable monotonic function the behavioral distance has the important property that two systems are at zero distance if and only if they are bisimilar moreover for any given threshold we find that systems with behavioral distances bounded by the threshold are equivalent in addition we show that two system combinators parallel composition and product are nonexpansive with respect to our behavioral distance which makes compositional verification possible the theory developed here is applicable to the quantitative verification approximate reduction and reliability analysis of fuzzy transition systems

factorization problems for nests factorization methods and characterizations of the universal factorization property let m be a von neumann algebra and let be a nest in m we consider the problem of factoring an invertible element s of m as s wa where w is a unitary element in m and both a and a 1 are elements of m which also belong to alg it is known that this is not always possible however using a variant of the lu decomposition for matrices we show that if is an injective nest and s is an invertible operator then there exists an isometry w such that both s 1w and w s belong to alg we characterize when an invertible operator factors with respect to an injective nest we also prove a result which simultaneously generalizes results of arveson and gohberg and krein finally we give a number of characterizations of those nests within a factor such that every invertible operator factors with respect to the nest

brief paper bisimilarity control of partially observed nondeterministic discrete event systems and a test algorithm in this paper the bisimilarity control of discrete event systems dess under partial observations is investigated where the plant and the specification are allowed to be nondeterministic a notation of simulation based controllability and a synchronization scheme for the supervised system are formalized based on the simulation relation between the specification and the plant it is shown that the existence of bisimilarity supervisors is characterized by the notions of the simulation based controllability and the language observability which extends the traditional results of supervisory control from language equivalence to bisimulation equivalence in addition a polynomial algorithm to test the simulation based controllability is developed by constructing a computing tree this algorithm together with the test of language observability can be used to check the existence of bisimilarity supervisors

nest algebras and similarity transformations in recent years the theory of algebras of operators on hilbert space has been stimulated by developments in the theory of quasitriangularity andersen 1 has shown that up to unitary equivalence there is only one continuous quasitrianguilar algebra we use this to provide the following answer to a question posed by j r ringrose approximately 20 years ago similar continuous nests on separable hilbert space can fail to be unitarily equivalent theorem 2 2 a consequence is the existence of a nonhyperintransitive compact operator corollary 2 3 which answers a question of kadison and singer 12 and of gohberg and krein 11 we extend our initial theorem to show that arbitrary continuous nests are similar theorem 2 10 and that every maximal nest is similar to a multiplicity one nest theorem 2 11 a consequence is that every compact operator is similar to a hyperintransitive compact operator corollary 2 12 the similarity transformation can be induced by an arbitrarily small compact perturbation of a unitary operator the methods of section 2 apply only to the continuous parts of nests for general results the atomic core part must be dealt with in section 3 different methods are developed for this purpose again utilizing andersen s results these are used in section 4 to prove that a complete nest x admits an arveson factorization for every positive invertible operator if and only if x is countable as a family of subspaces theorem 4 7 a consequence is that if x is an uncountable nest with atomic core then some similarity transformation of x has a continuous part this could not be deduced from section 2 these methods also yield a weak factorization result which concludes the paper it should be noted that a negative resolution to the ringrose question was conjectured in recent years by several mathematicians including w arveson and j ringrose also many of the results presented in this paper were announced in an a m s bulletin article 16 finally we wish to thank the referee for suggesting that the original manuscript could be condensed and improved

time varying optimal disturbance minimization in presence of plant uncertainty the optimal robust disturbance rejection problem plays an important role in feedback control theory here its time varying version is solved explicitly in terms of duality and operator theory in particular the optimum is shown to satisfy a time varying allpass property moreover optimal performance is given in terms of the norm of a bilinear form the latter depends on a lower triangular projection and a multiplication operator defined on special versions of spaces of compact operators

value passing ccs with noisy channels value passing ccs a full version of milner s ccs is a process algebra in which actions consist of sending and receiving values through noiseless communication channels the full calculus is a succinct yet expressive language for the specification and verification of reactive systems taking into account the reality of channel noise in reactive systems in this paper we introduce an extension of value passing ccs called value passing ccs with noisy channels vccs n in which noise is described by a probability distribution over the values after presenting the reduction operational semantics and labelled operational semantics of vccs n we develop the theory of behavioural equivalence by introducing barbed equivalence barbed congruence bisimilarity and full bisimilarity in particular we show that barbed equivalence and barbed congruence coincide with bisimilarity and full bisimilarity respectively based upon the labelled operational semantics of vccs n we establish a probabilistic modal logic for expressing system properties and show its connection with the notion of bisimilarity finally we use vccs n to model a communication protocol for ensuring the reliable transmission of data across an error prone channel