Sulľapplicazione della funzione ellitticap u alla teoria dei poligoni di poncelet

Abstract  In this paper we study strongly continuous positive semigroups on particular classes of weighted continuous function space on a locally compact Hausdorff space X having a countable base. In particular we characterize those positive semigroups which are the transition semigroups of suitable Markov processes. Some applications are also discussed. Keywords Positive semigroup, Markov transition function, Markov process, Weighted continuous function space, Degenerate second order differential operator Mathematics Subject Classification (2000) 47D06, 47D07, 60J60     

The Spectral Mapping Theorem for Evlution Semigroups on L p Associated with Strongly Continuous Cocycles

In this note we prove the spectral mapping theorem for certain evolution semigroups. Specifically, we study the evolution semigroup on L^p(Theta,mu;X), 1≤p相似文献   

An essentially saturated surface not of Kahler type

It is shown that if X is an Inoue surface of type S_M then theirreducible components of the Douady space of Xⁿ are compact,for all n 0. This gives an example, sought by Moosa [J. ReineAngew. Math. 586 (2005) 1–20], of an essentially saturatedcompact complex manifold (in the sense of model theory) thatis not of Kähler type. Among the known compact complexsurfaces without curves, these are the only examples.     

Full Crossed Products by Coactions, C0(X)-Algebras and C*-Bundles

Let be a coaction of a locally compact group G on a C*-algebraA. We show that if I is a -invariant ideal in A, then for full crossed products, as Landstadet al. have done for spatial crossed products by coactions.We prove that for suitable coactions, the crossed products ofC₀(X)-algebras are again C₀(X)-algebras, and the crossed productsof continuous C*-bundles by a locally compact group are againcontinuous C*-bundles. 1991 Mathematics Subject Classification46L55.     

Uniform semigroups and fixed point properties

LetS be a uniform semigroup (this includes all topological groups and affine semigroups). We show that a certain space of uniformly continuous functions onS has a left invariant mean iffS has the fixed point property for uniformly continuous affine actions ofS on compact convex sets. This is closely related to but independent of the results of T. Mitchell in [13] and A. Lau in [10]. Interesting examples and consequences are given for the special cases of topological groups and affine convolution semigroups of probability measures on a locally compact semigroup or group. Research Supported by NSERC of Canada Grant No. A8227.     

The Amenability of Measure Algebras

In this paper we shall prove that the measure algebra M(G) ofa locally compact group G is amenable as a Banach algebra ifand only if G is discrete and amenable as a group. Our contributionis to resolve a conjecture by proving that M(G) is not amenablein the case where the group G is not discrete. Indeed, we shallprove a much stronger result: the measure algebra of a non-discrete,locally compact group has a non-zero, continuous point derivationat a certain character on the algebra.     

Extensions of Isometric Dual Representations of Semigroups

Let T be a dual representation of a suitable subsemigroup Sof a locally compact abelian group G by isometries on a dualBanach space X=(X_*)^*. It is shown that (X, T) can be extendedto a dual representation of G on a dual Banach space Y containingX, and that this extension can be done in a canonical way. Inthe case of a representation by *-monomorphisms of a von Neumannalgebra, the extension is a representation of G by *-automorphismsof a von Neumann algebra.     

Ergodic properties of operator semigroups in general weak topologies

The aim of this paper is to study ergodic properties (i.e., properties about the limit of Cesàro averages) of a semigroup of bounded linear operators on a Banach space X, which is assumed to be continuous and locally integrable in the sense of a certain general weak topology of X. Then the results are applied to particular examples, such as locally strongly integrable semigroups, their dual semigroups, and the tensor product semigroup of two (C₀)-semigroups.     

Continuous Bundles of C*-Algebras with Discontinuous Tensor Products

For each non-exact C*-algebra A and infinite compact Hausdorffspace X there exists a continuous bundle B of C*-algebras onX such that the minimal tensor product bundle AB is discontinuous.The bundle B can be chosen to be unital with constant simplefibre. When X is metrizable, B can also be chosen to be separable.As a corollary, a C*-algebra A is exact if and only if A Bis continuous for all unital continuous C*-bundles B on a giveninfinite compact Hausdorff base space. The key to proving theseresults is showing that for a non-exact C*-algebra A there existsa separable unital continuous C*-bundle B on [0,1] such thatA B is continuous on [0,1] and discontinuous at 1, a counter-intuitiveresult. For a non-exact C*-algebra A and separable C*-bundleB on [0,1], the set of points of discontinuity of A B in [0,1]can be of positive Lebesgue measure, and even of measure 1.2000 Mathematics Subject Classification 46L06 (primary), 46L35(secondary).     

Convolution semigroups of states

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C*-bialgebra, the noncommutative counterpart of a locally compact semigroup. On locally compact quantum groups we obtain a bijective correspondence between such convolution semigroups and a class of C ₀-semigroups of maps which we characterise. On C*-bialgebras of discrete type we show that all weakly continuous convolution semigroups of states are automatically norm-continuous. As an application we deduce a known characterisation of continuous conditionally positive-definite Hermitian functions on a compact group.     

Adjoint bi-continuous semigroups and semigroups on the space of measures

For a given bi-continuous semigroup (T(t)) _t⩾0 on a Banach space X we define its adjoint on an appropriate closed subspace X° of the norm dual X′. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ(X°,X). We give the following application: For Ω a Polish space we consider operator semigroups on the space C_b(Ω) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(Ω) of bounded Baire measures (endowed with the weak*-topology). We show that bi-continuous semigroups on M(Ω) are precisely those that are adjoints of bi-continuous semigroups on C_b(Ω). We also prove that the class of bi-continuous semigroups on C_b(ω) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. In general, if is not a Polish space this is not the case.     

Essential Equivariant Maps and Borsuk-Ulam Theorems

A full characterization is given of those compact Lie groupsG with the property that every G-map XX on a finite-dimensionalG-complex X of finite orbit type, X^G = Ø, is (non-equivariantly)essential. For arbitrary G, conditions are given on the G-spaceX which guarantee this property. Finally, conditions are givenfor the non-existence of a G-map XY inducing a homotopy equivalenceX^GY^G on the fixed point sets. These results have applicationsto critical point theory of almost G-invariant functionals.     

Weierstrass Points on X0(pM) and Supersingular j-Invariants

Weierstrass points are special points on a Riemann surface thatcarry a lot of information. Ogg studied such points on X₀(pM)(for M such that X₀(M) has genus zero and p prime with p M),and he proved that if Q is a Q-rational Weierstrass point onX₀(pM), then its reduction modulo p is supersingular. The papershows that, for square-free M on the list, all supersingularj-invariants are obtained in this way. Furthermore, for mostcases where M is prime, the explicit correspondence betweenWeierstrass points and supersingular j-invariants in characteristicp is described. Along the way, a useful formula of Rohrlichfor computing a certain Wronskian of modular forms modulo pis generalized.     

A complete theory for jointly continuous nonlinear semigroups on a complete separable metric space

For a jointly continuous semigroup of transformations on a complete separable metric space X an induced semigroup of linear transformations on an appropriate space of measures is defined. A complete characterization of generators of such semigroups is given and it is shown how to construct a jointly continuous semigroup on X from a generator taken from this characterized collection.     

On Holomorphic Principal Bundles Over a Compact Riemann Surface Admitting a Flat Connection, II

Holomorphic principal bundles over a compact Riemann surfaceX that admits a flat connection are considered. A holomorphicG-bundle over X, where G is a connected semisimple linear algebraicgroup over C, admits a flat connection if and only if the adjointvector bundle admits one. More generally, for a complex reductivegroup G, the necessary and sufficient condition on a G-bundleto admit a flat connection is described. This simplifies thecriterion obtained by the authors and given in Math. Ann. 322(2002) 333–346. 2000 Mathematics Subject Classification53C05, 32L05.     

Strongly e-movable convergence and spaces of ANR's

Let X be a metric space and let ANR(X) denote the hyperspace of all compact ANR's in X. This paper introduces a notion of a strongly e-movable convergence for sequences in ANR(X) and proves several characterizations of strongly e-movable convergence. For a (complete) separable metric space X we show that ANR(X) with the topology induced by strongly e-movable convergence can be metrized as a (complete) separable metric space. Moreover, if X is a finite-dimensional compactum, then strongly e-movable convergence induces on ANR(X) the same topology as that induced by Borsuk's homotopy metric.For a separable Q-manifold M, ANR(M) is locally arcwise connected and A, B ? ANR(M) can be joined by an arc in ANR(M) iff there is a simple homotopy equivalence ?: A → B homotopic to the inclusion of A into M.     

More stratifiable function spaces

If X is a compact-covering image of a closed subspace of product of a σ-compact Polish space and a compact space, then Ck(X,M), the space of continuous maps of X into M with the compact-open topology, is stratifiable for any metric space M.If X is σ-compact Polish, K is compact and M metric then every point of Ck(X×K,M) has a closure-preserving local base, and hence this function space is M₁.     

Topologie Des (M - 2)-Courbes Reelles Symetriques

Let X be a non-singular real algebraic curve in CP² of evendegree. In this paper a refinement is proved of a theorem ofKharlamov about (M – 2)-curves that are invariants underthe projective involution. In particular, if the (M –2)-symmetric curve X satisfies the Arnold congruence, then eitherX or its twin is a separating curve. 2000 Mathematics SubjectClassification 14P25.     

A Trotter-Lie formula for compactly generated semigroups of nonlinear operators

A Trotter-Lie type formula for semigroups of nonlinear operators on a Banach space X into itself, which are generated by compact operators, is proved.