every completely polynomially bounded operator is similar to a contraction it is proved that a bounded operator on a hilbert space is similar to a contraction if and only if it is completely polynomially bounded this gives a partial answer to problem 6 of halmos bull amer math soc 76 1970 877 933 the set of completely bounded maps between c algebras is studied to obtain some structure representation and extension theorems for this class of maps these allow a characterization of the completely bounded representations on a hilbert space of any subalgebra of a c algebra to be obtained the result in the title follows by applying this characterization to the disk algebra

maximum likelihood identification of non stationary operational data abstract in operation modal analysis has become a valid alternative for structures where a classic input output test would be difficult if not impossible to conduct due to practical considerations measurements are sometimes performed in patches roving sensor setups instead of covering the entire structure at once in practice one is often confronted with non stationary ambient excitation sources e g wind traffic waves etc since the scaling of operational mode shape estimates depends on the unknown level of the ambient excitation an extra effort is required in order to correctly merge the different parts of the mode shapes in this contribution two different approaches for merging operational mode shapes from non stationary data are proposed both methods are based upon a single maximum likelihood estimation procedure for comparison and validation both techniques were applied to non stationary data sets obtained by scanning laser vibrometry as well as the z24 bridge bench mark data

boundary blow up for differential equations with indefinite weight we obtain results of existence and multiplicity of solutions for the second order equation x q t g x 0 with x t defined for all tis an element of 0 1 and such that x t infinity as t 0 and t 1 we assume g having superlinear growth at infinity and q t possibly changing sign on 0 1 c 2002 elsevier science usa all rights reserved

solution of the similarity problem for cyclic representations of c algebras in a paper from 1955 13 kadison considered the following problem is any bounded non selfadjoint representation 77 of a c algebra a on a hilbert space h similar to a representation i e does there exist an invertible operator t e b h such that tht t is a representation of a this problem is a natural counterpart to a problem considered by dixmier in 1950 9 is any bounded representation of a group g on a hilbert space similar to a unitary representation the group question was solved in the negative by kunze and stein in 1960 14 which in turn was based on previous work of ehrenpreis and mautner 21 the similarity problem for representations of c algebras is still open although a number of partial results have been obtained using the deep results of connes on infective von neumann algebras 7 and the characterization of nuclear c algebras given in 3 one gets the result fairly easily that every bounded representation of a nuclear c algebra is similar to a representation cf 2 th 3 5 and 5 th 4 1 the similarity problem for bounded cyclic representations of arbitrary c algebras was first considered by barnes in 1 he proved that when 77 is a bounded representation of a c algebra a on a hilbert space h such that 7v a and v a have a common cyclic vector i then there exists a closed infective operator t on h such that t and t are densely defined and such that x tht x t is a representation of a bunce sharpened this in 2 by proving that t can be chosen bounded but not necessarily with bounded inverse he also removed the condition that is cyclic for 7v a finally christensen proved in 5 that every irreducible bounded representation of a c algebra is similar to a representation these two results of bunce and christensen rely on an inequality due to pisier 16 cor 2 3 stating that when s is a bounded linear map from a c algebra a into a c algebra b then for all n e n and a an e a

boundary blow up elliptic problems with nonlinear gradient terms by karamata regular variation theory and perturbation method we show the exact asymptotical behaviour of solutions near the boundary to nonlinear elliptic problems u u q b x g u u 0 in u where is a bounded domain with smooth boundary in rn q 0 g c1 0 g 0 0 g is regularly varying at infinity with index with 0 and b is nonnegative nontrivial in which may be vanishing on the boundary

on the problem of stochastic experimental modal analysis based on multiple excitation multiple response data part ii the modal analysis approach in this part of the paper the stochastic multiple excitation multiple response modal analysis problem is considered the relationship between the actual structural and noise dynamics and their discrete special form armax type representation is studied for each one of the vibration displacement velocity and acceleration data cases and a novel and effective modal analysis approach is introduced that unlike previous schemes is capable of operating on any one of these types of data records by accounting for issues such as the required excitation signal type and stochastic model form algorithmic instability occurrence and other well known estimation difficulties model structure estimation and model validation as well as model reduction and analysis based on the dispersion analysis methodology introduced in the first part of the paper 1 the proposed approach not only overcomes the limitations and drawbacks of current schemes but also constitutes the first comprehensive procedure for stochastic multiple excitation multiple response experimental modal analysis the effectiveness of the approach is demonstrated through numerical experiments with structural systems characterized by well separated and closely spaced modes and data records of various lengths and signal to noise ratios comparisons with the classical frequency domain method and the deterministic eigensystem realization algorithm are also made and the approach is finally used for the experimental modal analysis of a three span beam from laboratory data

a dilation theory for polynomially bounded operators abstract in this paper we construct a special sort of dilation for an arbitrary polynomially bounded operator this enables us to show that the problem whether every polynomially bounded operator is similar to a contraction can be reduced to a subclass of it

in service identification of non linear damping from measured random vibration a non linearly damped single degree of freedom s d o f system under broadband random excitation is considered a procedure for in service identification of the damping characteristic from measured stationary response is described the procedure is based on the stochastic averaging method the explicit analytical solution is obtained for the integral equation which relates the desired damping characteristics to the apparent force in the shortened equation for the slowly varying response amplitude and thus to the measured probability density of the amplitude the approach is of a non parametric nature which makes it convenient for testing hypotheses of damping mechanisms from measured random vibration data extensive results of numerical tests for the procedure are presented

optimal uniqueness theorems and exact blow up rates of large solutions in this paper we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non linearity and combine these results with the localization method introduced in lopez gomez the boundary blow up rate of large solutions j differential equations 195 2003 25 45 to prove that any large solution l of u a x up p 1 a 0 must satisfy limx x0l x fx0 dist x i0 pp 1p 1p 1p 1p 1foreachx0 where fx0 t t 0sfx01p 1 p 1p 1ds i0 limt 0fx0 t fx0 t fx0 t 2 and fx0 is any smooth extension of the boundary normal section of a at x0 i e fx0 t a x0 tnx0 t 0 t 0 subsequently nx0 stands for the outward unit normal at x0 therefore the theory can be extended to cover the general case when fx0 l1p 1

general uniqueness results and variation speed for blow up solutions of elliptic equations let omega be a smooth bounded domain in r n we prove general uniqueness results for equations of the form delta u au b x f u in omega subject to u infty on partial omega our uniqueness theorem is established in a setting involving karamata s theory on regularly varying functions which is used to relate the blow up behavior of u x with f u and b x where b equiv 0 on partial omega and a certain ratio involving b is bounded near partial omega a key step in our proof of uniqueness uses a modification of an iteration technique due to safonov

an identification technique for non linear dynamical systems under stochastic excitations an identification technique is devised for sdof dynamical mechanical systems under random excitations the system is assumed to be governed by a non linear equation of motion in general form in which the restoring force and the dissipative terms are given by arbitrary power functions algebraic equations are obtained for the expectations of some suitable excitation and response quantities it is shown that these equations are valid for any stationary random excitations if the system attains the steady state based on these equations an identification technique has been devised and verified experimentally for white noise and coloured pink noise random excitations

large solutions for a semilinear elliptic problem with sign changing weights abstract this paper focuses on an elliptic boundary blow up problem with sign changing weights u a a g u x u where r n n 1 is a bounded smooth domain and 0 is a real parameter we verify that there exists 0 such that the problem has the minimal positive large solution for any 0 while no positive large solutions for any then by applying the local bifurcation theory we analyze the structure of the branch produced by the positive large solutions

a necessary and sufficient condition for existence of large solutions to semilinear elliptic equations we consider the semilinear equation u p x f u on a domain rn n 3 where f is a nonnegative nondecreasing continuous function which vanishes at the origin and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary for bounded we show that a nonnegative solution u satisfying u x as x exists if and only if the function s s0 f t dt satisfies 1 s 1 2 ds for unbounded including rn we show that a similar result holds where u x as x within and u x as x if p x decays to zero rapidly as x

multiplicity of positive solutions to boundary blow up elliptic problems with sign changing weights in this paper we consider the elliptic boundary blow up problem u a x ea x upin u on where is a bounded smooth domain of rn a a are positive continuous functions supported in disjoint subdomains of respectively p 1 and e 0 is a parameter we show that there exists e 0 such that no positive solutions exist when e e while a minimal positive solution exists for every e 0 e under the additional hypotheses that and intersect along a smooth n 1 dimensional manifold and a a have a convenient decay near we show that a second positive solution exists for every e 0 e if p n n 2 n 2 our proofs are mainly based on continuation methods

nondegeneracy and uniqueness for boundary blow up elliptic problems abstract in this paper we use for the first time linearization techniques to deal with boundary blow up elliptic problems after introducing a convenient functional setting we show that the problem u a x u p g x u in with u on has a unique positive solution for large enough and determine its asymptotic behavior as here p 1 a x is a continuous function which can be singular near and g x u is a perturbation term with potential growth near zero and infinity we also consider more general problems obtained by replacing u p by e u or a logistic type function f u

on centered and weakly centered operators abstract we show that if c is a contraction of spectral radius 1 then t is polynomially bounded if and only if the same is true of t c as a corollary we obtain that every invertible centered polynomially bounded operator is similar to a contraction we also prove a structure theorem for weakly centered operators that satisfy a hypothesis of a technical nature

completely contractive factorizations of c algebras abstract it is shown that a c algebra is nuclear if and only if the identity map can be approximated in the point norm topology by complete contractions factoring through matrix algebras

identification of the structure parameters using short time non stationary stochastic excitation abstract in this paper we propose an approach to the flexural stiffness or eigenvalue frequency identification of a linear structure using a non stationary stochastic excitation process the idea of the proposed approach lies within time domain input output methods the proposed method is based on transforming the dynamical problem into a static one by integrating the input and the output signals the output signal is the structure reaction i e structure displacements due to the short time irregular load of random type the systems with single and multiple degrees of freedom as well as continuous systems are considered

the effect of varying coefficients on the dynamics of a class of superlinear indefinite reaction diffusion equations abstract in this paper we analyze how the dynamics of a class of superlinear indefinite reaction diffusion equations varies as the nodal behavior of a coefficient changes to perform this analysis we use both theoretical and numerical tools the analysis aids the numerical study and the numerical study confirms and completes the analysis the numerics in addition provides us with some further results for which at first glance analytical tools are not available yet our main analytical result shows that the problem possesses a unique positive solution which is linearly asymptotically stable if the trivial state is linearly unstable and the model admits some positive solution this result is a relevant feature for superlinear indefinite problems since our numerical computations show how these models can have an arbitrarily large number of positive solutions if the trivial state is unstable

residually finite dimensional operator algebras abstract we study non selfadjoint operator algebras that can be entirely understood via their finite dimensional representations in contrast with the elementary matricial description of finite dimensional c algebras in the non selfadjoint setting we show that an additional level of flexibility must be allowed motivated by this peculiarity we consider a natural non selfadjoint notion of residual finite dimensionality we identify sufficient conditions for the tensor algebra of a c correspondence to enjoy this property to clarify the connection with the usual self adjoint notion we investigate the residual finite dimensionality of the minimal and maximal c covers associated to an operator algebra

varying bifurcation diagrams of positive solutions for a class of indefinite superlinear boundary value problems in this work we analyze the existence multiplicity and stability of positive solutions for a class of indefinite superlinear elliptic boundary value problems the main contribution of this paper consists in the change of mind inherent to the fact of adding the superlinear amplitude e as an unfolding parameter this change of mind allows us to unify many previous results obtained separately in the literature it helps us to realize the global structure of the set of positive steady states and provides us with a great variety of new general results our techniques can be applied to much more general equations and systems

the asymptotic behaviour of solutions with blow up at the boundary for semilinear elliptic problems abstract by constructing the comparison functions and the perturbed method it is showed that any solution u c 2 to the semilinear elliptic problems u k x g u x u satisfies lim d x 0 u x z d x 2 2 2 c 0 2 1 where is a bounded domain with smooth boundary in r n lim d x 0 k x d x c 0 2 c 0 0 2 2 g c 1 0 g 0 and g s s is increasing on 0 there exists 0 such that lim s g s g s 0 z s d t 2 g t s g t 0 t g s d s

structural identification from ambient vibration measurement using the multivariate ar model a procedure for identifying the dynamic characteristics of a structural system using the multivariate ar arv model is presented in the paper a least squares approach to determine the coefficient matrices of the arv model is proposed which is a modification of the traditional one the modification is based on the equivalence between the correlation function matrix for the responses of a linear system subjected to white noise input and the deterministic free vibration responses of the system then the dynamic characteristics of the system are evaluated directly from the coefficient matrices of the arv model by adopting the concept behind ibrahim s system identification technique the superiority of the proposed procedure over the traditional one is demonstrated through numerical studies on a six story shear building finally the present identification procedure is applied to identify the dynamic characteristics of a three span highway bridge from its ambient vibration responses subjected to traffic flow the validity of the present procedure is confirmed by the excellent agreement between the identified results obtained in the present study and those obtained from an impulse test

ein operatorwertiger hahn banach satz abstract we generalize arveson s extension theorem for completely positive mappings 1 to a hahn banach principle for matricial sublinear functionals with values in an injective c algebra or an ideal in b h we characterize injective w algebras by a matricial order condition we illustrate the matricial hahn banach principle by three applications 1 let a b b be unital c algebras b a subalgebra of a and b b injective if a b is a completely bounded self adjoint b bihomomorphism then it can be expressed as the difference of two completely positive b bihomomorphism 2 let m be a w algebra containing 1 h on a hilbert space h if m is finite and hyperfinite there exists an invariant expectation mapping p of b h onto m p is an extension of the center trace 3 combes 7 proved that a lower semicontinuous scalar weight on a c algebra is the upper envelope of bounded positive functionals we generalize this result to unbounded completely positive mappings with values in an injective w algebra

the boundary blow up rate of large solutions abstract in this paper we ascertain the blow up rate of the large solutions of a class of sublinear elliptic boundary value problems with a weight function in front of the nonlinearity that vanishes on the boundary of the underlying domain at different rates according to the point of the boundary x all previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of this hypothesis substantially simplified the mathematical analysis of the problem as it allowed constructing global sub and supersolutions in an open neighborhood of obtaining general results requires localizing at each particular point of the boundary making particularly involved the mathematical analysis of the problem

on the problem of stochastic experimental modal analysis based on multiple excitation multiple response data part i dispersion analysis of continuous time structural systems despite its importance and the undisputable significance of stochastic effects the problem of multiple excitation multiple response experimental modal analysis has thus far been almost exclusively considered within a deterministic framework in this paper a novel comprehensive and effective stochastic approach that unlike alternative schemes can operate on vibration displacement velocity or acceleration data is introduced the proposed approach is capable of effectively dealing with noise corrupted vibration data while also being characterized by unique features that enable it to overcome major drawbacks of current modal analysis methods and achieve high performance characteristics by employing a proper and mutually compatible force excitation signal type and stochastic model forms b an estimation scheme that circumvents problems such as algorithmic instability wrong convergence and high computational complexity while requiring no initial guess parameter values c effective model structure estimation and model validation procedures and d appropriate model transformation reduction and analysis procedures based on a novel dispersion analysis methodology this dispersion analysis methodology is a physically meaningful way of assessing the relative importance of the estimated vibrational modes based on their contributions dispersions to the vibration signal energy the effects of modal cross correlations are fully accounted for physical interpretations are provided in both the correlation and spectral domains and the phenomenon of negative dispersion modes is investigated and physically interpreted the effectiveness of the proposed approach is finally verified via numerical and laboratory experiments as well as comparisons with the classical frequency domain method and the deterministic eigensystem realization algorithm era the paper is divided into two parts the proposed dispersion analysis methodology is introduced in the first one whereas the complete stochastic experimental modal analysis approach is presented in the second 23

similarity problems in noncommutative polydomains abstract in this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials we obtain analogues of classical results such as rota s model theorem for operators with spectral radius less than one sz nagy characterization of operators similar to isometries or unitary operators and the refinement obtained by foias and by de branges and rovnyak for strongly stable contractions we also provide analogues of these results in the context of joint similarity of commuting tuples of positive linear maps on the algebra of bounded linear operators on a separable hilbert space an important role in this paper is played by a class of noncommutative cones associated with positive linear maps the fourier type representation of their elements and the constrained noncommutative berezin transforms associated with these elements it is shown that there is an intimate relation between the similarity problems and the existence of positive invertible elements in these noncommutative cones and the corresponding berezin kernels

moving force identification optimal state estimation approach existing techniques to identify moving forces exhibit the common weakness of having large fluctuations in the identified results a new method of moving force identification is developed in this paper making use of the dynamic programming technique to overcome this weakness the forces in the state space formulation of the dynamic system are identified in the time domain using a recursive formula based on several distributed sensor measurements and responses of the structure are reconstructed using the identified forces for comparison like all inverse problems the computation is ill conditioned however the dynamic programming technique inherently provides bounds to the ill conditioned forces and results from the simulation studies and laboratory work show great improvements over existing methods in the accuracy of identification