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1.
The quantum stochastic differential equation is considered on a unital C*-algebra, with separablenoise dimension space. Necessary conditions on the matrix ofbounded linear maps for the existence of a completely positivecontractive solution are shown to be sufficient. It is knownthat for completely positive contraction processes, k satisfiessuch an equation if and only if k is a regular Markovian cocycle.Feller refers to an invariance condition analogousto probabilistic terminology if the algebra is thought of asa non-commutative topological space. 2000 Mathematics SubjectClassification 81S25, 46L07, 46L53, 47D06. 相似文献
2.
The paper contains a final identification theorem for the genericK*-groups of finite Morley rank. 相似文献
3.
On sait associer à certaines structures de Poisson surRn, de 1-jet nul en 0, des actions de R2 sur Rn, donnéespar le rotationnel de leur partie quadratiqueet un autre champ de vecteurs. Lorsque ces actions sont nonrésonantes et hyperboliques, onmontre que ces structures sont quadratisables,en ce sens qu'il existe des coordonnées dans lesquelles,elles sont quadratiques. Dans le cas de la dimension 3, nosrésultats mènent à la non-dégénérescencegénérique des structures de Poisson quadratiquesà rotationnels inversibles. We can associate with some Poisson structures defined on Rnwith a zero 1-jet at zero, actions from R2 on Rn, given by thecurl of their quadratic part and another vectorfield. Assuming that those actions are hyperbolicsand without resonances, we give a normal formfor those structures. On R3, we prove that every quadratic Poissonstructure with invertible curl, is generically non degenerate. 相似文献
4.
Approximately Local Derivations 总被引:1,自引:0,他引:1
Certain linear operators from a Banach algebra A into a BanachA-bimodule X, which are called approximately local derivations,are studied. It is shown that when A is a C*-algebra, a Banachalgebra generated by idempotents, a semisimple annihilator Banachalgebra, or the group algebra of a SIN or a totally disconnectedgroup, bounded approximately local derivations from A into Xare derivations. This, in particular, extends a result of B.E. Johnson that local derivations on C*-algebras arederivations and provides an alternative proof of it. 相似文献
5.
A complete characterization of the categorical quotients of(P1)n by the diagonal action of SL(2, C) with respect to anypolarization is given by M. Polito, in SL(2, C)-quotientsde (P1)n, C. R. Acad. Sci. Paris Sér. I 321 (1995)15771582. In this paper, these categorical quotientsare obtained by certain linear systems on Pn3, dependingon the given polarization. 2000 Mathematics Subject Classification14L24, 14L30 相似文献
6.
The concept of Morita equivalence is generalized to the contextof locally C*-algebras. This generalizes a well-known theoremof Brown, Green and Rieffel, Pacific J. Math. 71 (1977) 349363.2000 Mathematics Subject Classification 46L08, 46L05. 相似文献
7.
** Email: rovas{at}uiuc.edu*** Email: luc_machiels{at}mckinsey.com**** Corresponding author. Email: maday{at}ann.jussieu.fr In this paper, we extend reduced-basis output bound methodsdeveloped earlier for elliptic problems, to problems describedby parameterized parabolic partial differentialequations. The essential new ingredient and the novelty of thispaper consist in the presence of time in the formulation andsolution of the problem. First, without assuming a time discretization,a reduced-basis procedure is presented to efficientlycompute accurate approximations to the solution of the parabolicproblem and relevant outputs of interest. In addition,we develop an error estimation procedure to a posteriorivalidate the accuracy of our output predictions. Second,using the discontinuous Galerkin method for the temporal discretization,the reduced-basis method and the output bound procedure areanalysed for the semi-discrete case. In both cases the reduced-basisis constructed by taking snapshots of the solutionboth in time and in the parameters: in that sense the methodis close to Proper Orthogonal Decomposition (POD). 相似文献
8.
If two operator algebras A and B are strongly Morita equivalent(in the sense of [5]), then their C*-envelopes C*(A) and C*(B)are strongly Morita equivalent (in the usual C*-algebraic sensedue to Rieffel). Moreover, if Y is an equivalence bimodule fora (strong) Morita equivalence of A and B, then the operation,YhA, of tensoring with Y, gives a bijection between theboundary representations of C*(A) for A and the boundary representationsof C*(B) for B. Thus the noncommutative Choquet boundariesof Morita equivalent A and B are the same. Other important objectsassociated with an operator algebra are also shown to be preservedby Morita equivalence, such as boundary ideals, the Shilov boundaryideal, Arveson's property of admissability, and the latticeof C*-algebras generated by an operator algebra. 1991 MathematicsSubject Classification 47D25, 46L05, 46M99, 16D90. 相似文献
9.
Nearly four hundred years ago, the cubic close-packing of equalspheres in R3 was discovered by Kepler [21], in which each spheretouches 12 others. In 1694, Gregory and Newton discussed thefollowing thirteen spheres problem. Can a rigid material spherebe brought into contact with 13 other such spheres of the samesize? Gregory believed yes, while Newton thoughtno. 1991 Mathematics Subject Classication 11H31,52C17. 相似文献
10.
It is shown that if S is an aperiodic random walk on the integers,S* is the Markov chain that arises when S is killed when itleaves the non-negative integers, and H+ is the renewal processof weak increasing ladder heights in S, then there is a 1:1correspondence between functions which are non-negative andsuperregular for S* and H+. This allows all the regular functionsfor S* to be described, and thus a result due to Spitzer tobe completed for the recurrent case. This result is then appliedto give a ratio limit theorem for Px(*=n)/P0{*=n}, where * isthe lifetime of S*, in the case when S drifts to , andthe right-hand tail of its step distribution is locallysub-exponential. 相似文献
11.
Let A be a unital maximal full algebra of operator fields withbase space [0, 1]k and fibre algebras . It is shown in this paper that the stable rankof A is bounded above by the quantity , where sr means stable rank. Usingthe above estimate, the stable ranks of the C*-algebras of the(possibly higher rank) discrete Heisenberg groups are computed.2000 Mathematics Subject Classification 47L99. 相似文献
12.
On the Morita Equivalence of Tensor Algebras 总被引:4,自引:0,他引:4
We develop a notion of Morita equivalence for general C*-correspondencesover C*-algebras. We show that if two correspondences are Moritaequivalent, then the tensor algebras built from them are stronglyMorita equivalent in the sense developed by Blecher, Muhly andPaulsen. Also, the Toeplitz algebras are strongly Morita equivalentin the sense of Rieffel, as are the CuntzPimsner algebras.Conversely, if the tensor algebras are strongly Morita equivalent,and if the correspondences are aperiodic in a fashion that generalizesthe notion of aperiodicity for automorphisms of C*-algebras,then the correspondences are Morita equivalent. This generalizesa venerated theorem of Arveson on algebraic conjugacy invariantsfor ergodic, measure-preserving transformations. The notionof aperiodicity, which also generalizes the concept of fullConnes spectrum for automorphisms, is explored; its role inthe ideal theory of tensor algebras and in the theory of theirautomorphisms is investigated. 1991 Mathematics Subject Classification:46H10, 46H20, 46H99, 46M99, 47D15, 47D25. 相似文献
13.
The purpose of this paper is to give a detailed study of thebasic theory of C*-categories. The study includes some examplesof C*-categories that occur naturally in geometric applications,such as groupoid C*-categories, and C*-categories associatedto structures in coarse geometry. We conclude the paper witha brief survey of Hilbert modules over C*-categories. 2000 MathematicalSubject Classification: 18D99, 46L05, 46L08. 相似文献
14.
For any nonnegative self-adjoint operators A and B in a separableHilbert space, the Trotter-type formula is shown to converge strongly in the norm closureof dom (A1/2) dom (B1/2 for some subsequence and for almostevery t R. This result extends to the degenerate case, andto Kato-functions following the method of T. Kato (see Trotter'sproduct formula for an arbitrary pair of self-adjoint contractionsemigroup, Topics in functional analysis (ed. M. Kac,Academic Press, New York, 1978) 185195). Moreover, therestrictions on the convergence can be removed by consideringfunctions other than the exponential. 2000 Mathematics SubjectClassification 47D03 (primary), 47B25 (secondary). 相似文献
15.
It is shown that a 1-factorization of Kn with a doubly transitiveautomorphism group on vertices is either the affine line-parallelismof AG(d, 2), or one of three sporadic exampleswith n = 6, 12 or 28. The full automorphism groups are respectivelyAGL (d, 2) (the holomorph of an elementary abelian group oforder 2d), PGL(2,5), PSL(2,11) and PL(2,8). 相似文献
16.
In a beautiful result, Herrero (D. A. Herrero, Normallimits of nilpotent operators, Indiana Univ. Math. J.23 (1973/74) 10971108) showed that a normal operatoron l2 lies in the closure of the set of nilpotent operatorsif and only if its spectrum is connected and contains zero.In the quest for an automatic continuity result for algebrahomomorphisms between C* -algebras, Dales showed that, if adiscontinuous algebra homomorphism : A u exists between C*-algebrasA and u, and if (A) is dense in u, then there is a C*-algebrau2 with a dense subalgebra N u2 such that every x N is quasinilpotent(see p. 685 of H. G. Dales, Banach algebras and automatic continuity,London Mathematical Society Monographs 24, Oxford UniversityPress, 2001). (A discontinuous homomorphism 2: A2 u2 can bedefined with the same basic properties as , but the revisedtarget space u2 has a dense subalgebra consisting of quasinilpotentelements.) As remarked by Dales, no such C*-algebra was thenknown; but here we present one. Indeed, using the full powerof Herrero's result, one may arrange that every x N is nilpotent.The C*-algebra is constructed in a neat way; itis most naturally constructed as a non-separable, concrete C*-algebraof operators on a separable Hilbert space K but one can arrangethat the algebra u itself be separable if desired. 2000 MathematicsSubject Classification 47C15, 46H40 (primary), 47A10, 46L06,46L05, 46H35 (secondary). 相似文献
17.
We show that the norms of the sequence of spectral projectionsof certain non-self-adjoint ordinary differential operatorscannot be polynomially bounded. The proof involves the investigationof tame bi-orthogonal systems in Banach spaces.2000 Mathematics Subject Classification 34L10, 46B15. 相似文献
18.
Transformations Between Sturm-Liouville Problems with Eigenvalue Dependent and Independent Boundary Conditions 总被引:1,自引:0,他引:1
Binding Paul A.; Browne Patrick J.; Watson Bruce A. 《Bulletin London Mathematical Society》2001,33(6):749-757
Explicit relationships are given connecting almostisospectral Sturm-Liouville problems with eigen-value dependent,and independent, boundary conditions, respectively. Applicationis made to various direct and inverse spectral questions. 2000Mathematics Subject Classification 34B24, 34L05, 47E05. 相似文献
19.
Grothendieck's Inequalities for Real and Complex JBW*-Triples 总被引:1,自引:0,他引:1
Peralta Antonio M.; Palacios Angel Rodriguez 《Proceedings London Mathematical Society》2001,83(3):605-625
We prove that, if and >0, if V and W are complex JBW*-triples (with preduals V* andW*, respectively), and if U is a separately weak*-continuousbilinear form on V x W, then there exist norm-one functionals1, 2 V* and 1, 2 W* satisfying
for all (x, y) V x W. Here, for a norm-one functional on acomplex JB*-triple V, |·| stands for the prehilbertianseminorm on V associated to given by for all x W, where z V** satisfies z = |z| =1. We arrive at this form of Grothendieck's inequalitythrough results of C.-H. Chu, B. Iochum, and G. Loupias, andan amended version of the little Grothendieck's inequalityfor complex JB*-triples due to T. Barton and Y. Friedman. Wealso obtain extensions of these results to the setting of realJB*-triples. 2000 Mathematical Subject Classification: 17C65,46K70, 46L05, 46L10, 46L70. 相似文献
20.
In this paper the authors develop a new approach to the problemof propagation of smallness for harmonic functionsin arbitrary domains, in Rn (n 2). The main result of thispaper is a certain logarithmic-convexity relation for the L2-normsof harmonic functions. As a consequence, new kinds of uniquenessresults for harmonic functions are obtained. The method worksalso for analytic functions in C, with Lp-norms (p > 0).1991 Mathematics Subject Classification 31B05. 相似文献