applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

on the continuity of the map ϑ ϑ from the predual of a w algebra abstract let be elements in the predual of a w algebra for their absolute value parts the estimate 2 1 2 is obtained

the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

robust h disturbance minimization by duality abstract the nonstandard optimization problem inf sup w i pq e i vpq e i 0 2 q h n n plays a basic role in robust feedback analysis here its solutions are characterized using banach space duality theory and shown to satisfy a flatness or allpass condition

duality theory of robust disturbance attenuation abstract the nonstandard minimization problem inf q h w 1 pq vpq underlies many questions of robust control here its solutions are characterized using banach space duality theory and shown to be allpass the results are applied to the optimization of weighted sensitivity to disturbances in feedback systems subject to large plant uncertainty

some physical structures for the 2 1 dimensional boussinesq water equation with positive and negative exponents in this paper a mathematical method is constructed to study two variants of the two dimensional boussinesq water equation with positive and negative exponents in terms of travelling wave solutions the partial differential equations are transformed to nonlinear ordinary differential equations exact solutions are then derived for various cases to describe the different physical structures such as compactons solitons solitary patterns and periodic solutions the exponent of the wave function u and the ratio of the two coefficients a and b in the boussinesq equation are shown to qualitatively determine the physical structures of the solutions

a note on essential spectra and norms of mixed hankel toeplitz operators in this brief hankel toeplitz operators which occur in feedback theory e g in the minimization of mixed h sensitivity and complementary sensitivity will be considered a method of computing their spectra eigenvectors and norms will be presented for infinite dimensional systems subject to continuous weightings

well posedness of h optimal control problems this paper considers the effect of perturbations of a nominal single input single output linear plant or a band of uncertainty on the solution to certain frequency domain optimal control problems weighted h infty sensitivity minimization mixed and robust sensitivity minimization will be considered along with problems of more general type a brief discussion of h p optimal control problems will also be given typical examples will be presented where optimal sensitivity does not depend continuously on the plant ill posedness and conditions for well posedness will be given it is demonstrated that similar discontinuities can occur for more general problems also suggested are ways of defining an optimization problem so that continuous dependence of the infimum is ensured

polynomials on banach lattices and positive tensor products abstract this paper is the first systematic study of homogeneous polynomials on banach lattices a variety of new banach spaces and banach lattices of multilinear maps homogeneous polynomials and operators are introduced the main technique is to employ positive tensor products and quotients of positive tensor products our theorems generalize the results on orthogonally additive polynomials by benyamini lassalle and llavona 2006 in 4 the results by grecu and ryan 2005 in 14 and the results by sundaresan 1991 in 23

superoptimal analytic approximations of matrix functions we study the approximation of a bounded matrix valued function g on the unit circle by functions q bounded and analytic in the unit disc we show that if g is continuous then there is a unique q for which the error g q has a strong minimality property involving not only the l norm of g q but also the suprema of its subsequent singular values we obtain structural properties of the error g q and show that certain smoothness properties of g are inherited by q e g membership of besov spaces

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

optimal model matching control for time delay systems model matching control for time delay systems is formulated as an optimization problem in h2 norm space as well as h norm space wiener hopf techniques and the theory of optimal interpolation are successfully employed to treat this model matching problem including perfect and imperfect model matching cases prior to this work for time delay systems only the problem of perfect model matching control had been considered and no attempt had been made to examine that of imperfect model matching control with the optimization approach presented here an optimal model matching control scheme is constructed for the imperfect model matching case to produce perfect model matching results whenever possible

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

a spectral characterization of h optimal feedback performance and its efficient computation abstract we study the spectral properties of a toeplitz hankel operator which arises in the context of the mixed sensitivity h optimization problem and whose largest eigenvalue characterizes the optimal achievable performance 0 the existence of such an operator was first shown by verma and jonckheere 26 who also noted the potential numerical advantage of computing eo through its eigenvalue characterization rather than through the iteration here we investigate this operator in detail with the objective of efficiency computing its spectrum we define an adjoint linear quadratic problem that involves the same toeplitz hankel operator as shown by jonckheere and silverman 13 16 consequently a finite polynomial algorithm allows 0 to be characterized as simply as the largest root of a polynomial finally a computationally more attractive state space algorithm emerges from the h t 8 lq relationship this algorithm yields a very good accuracy evaluation of the performance 0 by solving just one algebraic riccati equation thorough exploitation of this algorithm results in a drastic computation reduction with respect to the standard e iteration

powers of quasi banach lattices and orthogonally additive polynomials abstract the paper aims to examine convexity and concavity conditions for homogeneous orthogonally additive polynomials in quasi banach lattices we characterize p q convex quasi banach lattice by the property that every positive orthogonally additive polynomial defined on such lattice is p q convex as well as obtain some versions of krivine factorization result and grothendieck s inequality for orthogonally additive polynomials in quasi banach lattices

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

multilinear forms subsymmetric polynomials and spreading models on banach spaces abstract some applications of ramsey theory to the study of multilinear forms and polynomials on banach spaces are given related to the existence of lower l q estimates of sequences we give an explicit representation of subsymmetric polynomials in banach spaces with subsymmetric basis finally we apply our results to get approximation of polynomials by subsymmetric polynomials and to the problem of stabilization of a certain chain of algebras generated by polynomials

weakly continuous mappings on banach spaces abstract it is shown that every n homogeneous continuous polynomial on a banach space e which is weakly continuous on the unit ball of e is weakly uniformly continuous on the unit ball of e applications of the result to spaces of polynomials and holomorphic mappings on e are given

an asymptotic theory for a class of initial boundary value problems for weakly nonlinear wave equations with an application to a model of the galloping oscillations of overhead transmission the aim of this paper is to contribute to the foundation of the asymptotic methods for initial boundary value problems and initial value problems for weakly nonlinear hyperbolic partial differential equations of order two in this paper an asymptotic theory for a class of initial boundary value problems for weakly nonlinear wave equations is presented the theory implies the well posedness of the problem in the classical sense and the validity of formal approximations on long timescales as an application of the theory an initial boundary value problem for a rayleigh wave equation is studied in detail using a two timescale perturbation method from an aeroelastic analysis it is shown that this initial boundary value problem may be regarded as a model describing the growth of wind induced oscillations of overhead transmission lines

the asymptotic theory of global solutions for semilinear wave equations in three space dimensions abstract this paper deals with the asymptotic theory of initial value problems for semilinear wave equations in three space dimensions the well posedness and validity of formal approximations about time t are discussed in the classical sense of c2 the results describe the validity of formal global solutions using a time scale perturbation method an application of the asymptotic theory is given to analyze a special wave equation in three space dimensions

approximation by analytic matrix functions the four block problem abstract the four block problem is a generalization of nehari s problem for matrix functions it plays an important role in h optimal control theory it is well known that nehari s problem for a continuous scalar function has a unique solution however in the matrix case the situation is quite different v v peller and n j young 1994 j funct anal 120 300 343 studied superoptimal solutions of nehari s problem they minimize not only the l norm of the corresponding matrix function but also the essential suprema of all further singular values it was shown that for h c matrix functions nehari s problem has a unique superoptimal solution in this paper we study superoptimal solutions of the four block problem and we find a natural condition under which such a superoptimal solution is unique our result is new even in the case of nehari s problem we study some related problems such as thematic factorizations invariance of indices and inequalities between the singular values of the four block operator and the superoptimal singular values

extreme polynomials and multilinear forms onl1 abstract given a 2 homogeneous polynomialp x y ax2 by2 cxywith real coefficients let p rand p cdenote the norms ofpon the real and complex banach spacel21 respectively we show p r p c and obtain a sufficient and necessary condition on the coefficientsa b andcforpto have norm 1 applying these results we characterize extreme points of the unit ball of p 2l1 for the real banach spacel21and examine them for the complex banach spacel21 we apply them to find extreme points and strongly extreme points of the unit ball of p 2l1 and get an extremal 2 homogeneous polynomial onl1that is not an extreme point we also characterize extreme points and strongly extreme points of the unit ball of l ml1 or l ml1 0 1

the non commutative flow of weights on a von neumann algebra abstract the flow of weights of connes and takesaki is a canonical functor from the category of separable factors to the category of ergodic flows the non commutative flow of weights is another canonical functor from the category of separable factors to the category of covariant systems of semi finite von neumann algebras equipped with trace scaling one parameter automorphism groups with conjugations as morphisms the constructions of these two functors are very similar the flow of weights functor is obtained by looking at all semi finite normal weights on a factor with the murray von neumann equivalence relation the non commutative flow of weights functor is obtained by relating an arbitrary pair of faithful semi finite normal weights by the connes cocycle not only does this construction put a period to the search for a canonical construction of the core of a factor of type iii but it also allows us to put the characteristic square of a factor obtained by katayama sutherland and takesaki in a new perspective the power of this new approach is seen in an ultimate solution to a long standing question of extending the extended modular automorphism of a dominant weight to an arbitrary weight which has been left open ever since the introduction of extended modular automorphisms by connes and takesaki over 20 years ago the construction of the functor ties together the theory of l p spaces of haagerup kosaki hilsum terp and izumi to the structure theory of a factor of type iii in fact the non commutative flow of weights is obtained by the analytic continuation of l p spaces to a pure imaginary value of p

algebraic tensor products and internal homs of noncommutative lp spaces abstract we prove that the multiplication map is an isometric isomorphism of quasi banach m m bimodules here is the noncommutative l p space of an arbitrary von neumann algebra m and m denotes the algebraic tensor product over m equipped with the quasi projective tensor norm but without any kind of completion similarly the left multiplication map is an isometric isomorphism of quasi banach m m bimodules where hom m denotes the algebraic internal hom in particular we establish an automatic continuity result for such maps applications of these results include establishing explicit algebraic equivalences between the categories of modules of junge and sherman for all p 0 as well as identifying subspaces of the space of bilinear forms on spaces this paper is also available at arxiv 1309 7856v2

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

duality theory for mimo robust disturbance rejection banach space duality theory is used to characterize the solutions of a nonstandard h sup infinity optimization problem which is shown to be allpass in general and unique in the single input single output siso ease the theory leads to a numerical solution of duality and convex optimization which is applied to an example for a limiting case of sharp cutoff filters an explicit solution of the optimal robust disturbance attenuation problem ordap resembling the two arc theorem of complex analysis is derived

remarks on complemented subspaces of von neumann algebras in this note we include two remarks about bounded not necessarily contractive linear projections on a von neumann algebra we show that if m is a von neumann subalgebra of b h which is complemented in b h and isomorphic to m m then m is injective or equivalently m is contractively complemented we do not know how to get rid of the second assumption on m in the second part we show that any complemented reflexive subspace of a c algebra is necessarily linearly isomorphic to a hilbert space

bases in the space of regular multilinear operators on banach lattices abstract for banach lattices e 1 e m and f with 1 unconditional bases we show that the monomial sequence forms a 1 unconditional basis of l r e 1 e m f the banach lattice of all regular m linear operators from e 1 e m to f if and only if each basis of e 1 e m is shrinking and every positive m linear operator from e 1 e m to f is weakly sequentially continuous as a consequence we obtain necessary and sufficient conditions for which the m fold fremlin projective tensor product e 1 e m resp the m fold positive injective tensor product e 1 e m has a shrinking basis or a boundedly complete basis

weight selection in feedback design with degree constraints we present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint performance is cast as an interpolation problem with bounded analytic functions minimizers of a certain weighted entropy functional provide interpolants having degree less than the number of constraints the choice of weight parameterizes all such bounded degree solutions however the relationship between the weights and the shape of corresponding transfer functions is not direct thus in this paper we develop a formalism that guides weight selection

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

on initial boundary value problems for weakly semilinear telegraph equations asymptotic theory and application in this paper an asymptotic theory for a class of initial boundary value problems for weakly semilinear telegraph equations is presented the theory implies the well posedness of the problem and the validity of formal approximations on long time scales as an application of the theory an initial boundary value problem for the equation u tt u xx u varepsilon u 3 0 is considered to construct an o varepsilon approximation of the solution of this problem a two time scale perturbation method is applied

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

orthogonally additive polynomials on spaces of continuous functions we show that for every orthogonally additive homogeneous polynomial p on a space of continuous functions c k with values in a banach space y there exists a linear operator s c k y such that p f s f n this is the c k version of a related result of sundaresam for polynomials on l p spaces

h2 optimal control of linear systems with tracking disturbance rejection constraints this paper considers the design of two degree of freedom linear multivariable controllers for four block matrix transfer functions with objectives pertaining to both random and deterministic signals the former are taken into account in the cost functional whereas the latter entail that the controller is constrained to solve a servomechanism problem involving a class of reference signals and two classes of disturbances the cost functional is set up by adding quadratic terms to the usual lqg wiener hopf cost in such a way as to ensure the existence of unique solutions even when the signals to be tracked rejected as well as models have poles on the imaginary axis the solutions of the servomechanism problem are explicitly parametrized by free stable rational and proper parameters under two sets of assumptions one which is necessary and sufficient for the existence of solutions and another stronger set which avoids kronecker products and the associated higher dimensional factorizations involved in

complemented subspaces of spaces of multilinear forms and tensor products abstract among other things we show that l q is isomorphic to a complemented subspace of the space of multilinear forms on l p 1 l p n where q 1 is given by 1 p 1 1 p n 1 q 1 the proof strongly depends on the l module structure of the spaces l p

mimo disturbance and plant uncertainty attenuation by feedback this paper investigates the ability of feedback to reduce plant and disturbance uncertainties in the multiple input multiple output mimo case by solving two fundamental problems posed by zames in the late seventies the first problem is termed the mimo extension of the optimal robust disturbance attenuation problem the second is a filtering of plant uncertainty two degree of freedom feedback problem the optimal solutions of these problems are characterized using banach space duality theory and shown to satisfy an allpass condition and an extremal identity moreover the duality description leads to a dual pair of optimizations and the introduction of two nonstandard matrix norms in particular the primal dual optimization reduces naturally to approximate finite dimensional convex optimizations within desired tolerance whereas the computation of the nonstandard matrix norms are shown to be equivalent to specific semi definite programming problems and a numerical solution based on convex programming is provided it is also shown using douglas range inclusion theorem that performance is a monotonic function of uncertainty and some qualitative implications for feedback are derived

operator theoretic approach to the optimal two disk problem the nonstandard two disk problem plays a fundamental role in robust feedback optimization here it is shown via banach space duality theory that its solutions satisfy an extremal identity and may be viewed as a dual extremal kernel of a particular l sup 1 optimization problem a novel operator theoretic framework to characterize explicitly its solutions is developed in particular the two disk optimization is shown to be equal to the induced norm of a specific operator defined on a projective tensor product space involving a non hilbert version of a vector valued h sup 2 space moreover this operator is shown to be a combination of multiplication and toeplitz operators under certain conditions existence of maximal vectors is established leading to an explicit formula for the optimal controller an infinite matrix representation with respect to a canonical basis is derived together with an algorithm to compute it the norm of the relevant operator is approximated by special finite dimensional optimizations whose solutions lead to solving semi definite programming problems involving the computation of a matrix projective tensor norm

complemented subspaces of spaces of multilinear forms and tensor products ii noncommutative lp spaces abstract we study tensor products of the schatten classes s p and their duals it is shown that if p 1 1 p k 1 q 1 1 then the space of multilinear forms b s p 1 s p k c contains a complemented subspace isometric to s q we construct explicit embeddings of s r n into s p n s q n for r 1 p 1 q 1 whose range is complemented by a natural norm one projection as a byproduct we compute the nuclear norm of some multiplication operators if r 1 1 p 1 q 1 with p q 1 then given an n by n matrix the nuclear norm of the multiplication operator h s p n h s q n is n times the norm of in s r n where r max 1 r a number of results on general noncommutative l p spaces are also included

polynomials in operator space theory the aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces for this purpose we take advantage of the basic fact that the space pm e of all m homogeneous polynomials on a vector space e can be identified with the algebraic dual of the m th symmetric tensor product m se given an operator space v we study several different types of completely bounded polynomials on v which form the operator space duals of m sv endowed with related operator structures of special interest are what we call haagerup kronecker and schur polynomials polynomials associated with different types of matrix products

pointwise tensor products of function spaces abstract by means of a mixture of linear and nonlinear techniques the paper treats quasi banach function spaces as l modules and studies the basic algebraical constructions and their interactions placing the emphasis on tensor products sample result if 0 y x z 0 is an exact sequence of l modules and homomorphisms where y and z are function spaces and v is another function space then the tensorized sequence 0 y v x v z v 0 is exact too

linear feedback systems and the graph topology it is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed loop stability and closed loop performance are robust properties in earlier works similar topological results were obtained by exploiting the existence of particular coprime factor system representations not known to exist in general by contrast the development here does not rely on any specific system representations systems are simply characterized as subspaces of norm bounded input output pairs and the analysis hinges on the underlying geometric structure of the feedback stabilization problem unlike other work developed within such a framework fundamental issues concerning the causality of feedback interconnections are discussed explicitly the key result of this paper concerns the difference between linear feedback interconnections with identical controllers in terms of a performance robustness related closed loop mapping upper and lower bounds on the induced norm of this difference are derived allowing for possibly infinite dimensional input output spaces and time varying behavior the bounds are both proportional to the gap metric distance between the plants which clearly demonstrates the gap to be an appropriate measure of the difference between open loop systems from the perspective of closed loop behavior to conclude an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

modular theory for bimodules abstract modular theory is developed for bimodules and its basic properties are established among them frobenius reciprocity is obtained in a fairly general setting

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

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

robust stabilization over communication channels in the presence of unstructured uncertainty this technical note is concerned with the problem of controlling plants over communication channels where the plant is subject to two types of unstructured uncertainty additive uncertainty and stable coprime factor uncertainty necessary lower bounds on the rate of transmission or channel capacity c for robust stabilization are computed explicitly in particular it is shown that the lower bound in the additive uncertainty case corresponds to a fixed point of a particular function in the stable coprime factor uncertainty case the derivation relies on linear fractional transformation concepts the results are important in determining the minimum channel capacity needed in order to stabilize plants subject to unstructured uncertainty over communication channels for instance the bounds obtained can be used to analyze the effect of uncertainty on the channel capacity an illustrative example is provided

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest

bases in spaces of multilinear forms over banach spaces fil dimant veronica universidad de san andres departamento de matematica y ciencias argentina