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1.
J. K. Brooks Kazuyuki Saitô JD Maitland Wright 《Rendiconti del Circolo Matematico di Palermo》2003,52(1):5-14
LetA be aC*-algebra with second dualA″. Let (φ
n)(n=1,...) be a sequence in the dual ofA such that limφ
n(a) exists for eacha εA. In general, this does not imply that limφ
n(x) exists for eachx εA″. But if limφ
n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ
n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for
positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem. 相似文献
2.
It is proved that ifX is a connected locally continuumwise connected coanalytic nowhere topologically complete space, then the hyperspace 2
X
of all nonempty compact subsets ofX is strongly universal in the class of all coanalytic spaces. Moreover, 2
X
is homeomorphic to Π2 ifX is a Baire space, and toQ∖Π1 ifX contains a dense absoluteG
δ-setG ⊂X such that the intersectionG ∩U is connected for any open connectedU ⊂X. (Here Π1, Π1⊂X are the standard subsets of the Hilbert cubeQ absorbing for the classes of analytic and coanalytic spaces, respectively.) Similar results are obtained for higher projective
classes.
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 35–51, July, 1997.
Translated by O. V. Sipacheva 相似文献
3.
It is shown that: (1) any action of a Moscow group G on a first countable, Dieudonné complete (in particular, on a metrizable) space X can uniquely be extended to an action of the Dieudonné completion γG on X, (2) any action of a locally pseudocompact topological group G on a b
f
-space (in particular, on a first countable space) X can uniquely be extended to an action of the Weil completion on the Dieudonné completion γX of X. As a consequence, we obtain that, for each locally pseudocompact topological group G, every G-space with the b
f
-property admits an equivariant embedding into a compact Hausdorff G-space. Furthermore, for each pseudocompact group G, every metrizable G-space has a G-invariant metric compatible with its topology. We also give a direct construction of such an invariant metric.
Received: June 22, 2000; in final form: May 22, 2001?Published online: June 11, 2002 相似文献
4.
A key tool in recent advances in understanding arithmetic progressions and other patterns in subsets of the integers is certain
norms or seminorms. One example is the norms on ℤ/Nℤ introduced by Gowers in his proof of Szemerédi’s Theorem, used to detect uniformity of subsets of the integers. Another
example is the seminorms on bounded functions in a measure preserving system (associated to the averages in Furstenberg’s
proof of Szemerédi’s Theorem) defined by the authors. For each integer k ≥ 1, we define seminorms on ℓ∞(ℤ) analogous to these norms and seminorms. We study the correlation of these norms with certain algebraically defined sequences,
which arise from evaluating a continuous function on the homogeneous space of a nilpotent Lie group on a orbit (the nilsequences).
Using these seminorms, we define a dual norm that acts as an upper bound for the correlation of a bounded sequence with a
nilsequence. We also prove an inverse theorem for the seminorms, showing how a bounded sequence correlates with a nilsequence.
As applications, we derive several ergodic theoretic results, including a nilsequence version of the Wiener-Wintner ergodic
theorem, a nil version of a corollary to the spectral theorem, and a weighted multiple ergodic convergence theorem. 相似文献
5.
Lutz Mattner 《Mathematische Semesterberichte》2010,193(2):11-16
The statements in the title are explained and proved, as a little exercise in elementary normed
vector space theory at the level of Chap. 5 of Dieudonné’s Foundations of Mathematical
Analysis. A connection to recent moment bounds for submartingales is sketched. 相似文献
6.
E. V. Schepin 《Mathematical Notes》1999,65(3):381-385
A proof of the Hilbert-Smith conjecture for a free Lipschitz action is given. The proof is elementary in the sense that it
does not rely on Yang’s theorem about the cohomology dimension of the orbit space of thep-acid action. The result turns out to be true for the class of spaces of finite Hausdorff volume, which is considerably wider
than Riemannian manifolds. As a corollary to the Lipschitz version of the Hilbert-Smith conjecture, the theorem asserting
that the diffeomorphism group of a finite-dimensional manifold has no small subgroups is obtained.
Translated fromMatermaticheskie Zametki, Vol. 65, No. 3, pp. 457–463, March, 1999. 相似文献
7.
A. V. Potepun 《Journal of Mathematical Sciences》1996,80(6):2328-2332
An order topology in vector lattices and Boolean algebras is studied under the additional condition of “closure by one step”
that generalizes the well-known “regularity” property of Boolean algebras and K-spaces. It is proved that in a vector lattice
or a Boolean algebra possessing such a property there exists a basis of solid neighborhoods of zero with respect to an order
topology. An example of a Boolean algebra without basis of solid neighborhoods of zero (an algebra of regular open subsets
of the interval (0, 1)) is given. Bibliography: 3 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 15 1995, pp. 213–220. 相似文献
8.
Marcelina Mocanu 《Complex Analysis and Operator Theory》2011,5(3):799-810
We prove a Poincaré inequality for Orlicz–Sobolev functions with zero boundary values in bounded open subsets of a metric
measure space. This result generalizes the (p, p)-Poincaré inequality for Newtonian functions with zero boundary values in metric measure spaces, as well as a Poincaré inequality
for Orlicz–Sobolev functions on a Euclidean space, proved by Fuchs and Osmolovski (J Anal Appl (Z.A.A.) 17(2):393–415, 1998).
Using the Poincaré inequality for Orlicz–Sobolev functions with zero boundary values we prove the existence and uniqueness
of a solution to an obstacle problem for a variational integral with nonstandard growth. 相似文献
9.
George K Francis 《Journal of Mathematical Analysis and Applications》1973,44(3):779-785
Certain nonlinear optimal control problems on a manifold can be represented in terms of a switchable family of regulated paths in the space of continuously differentiable vector fields. The methods also yield a theorem on the Dieudonné-Albrecht integrability conditions for non-autonomous first order differential equations on a Banach space. 相似文献
10.
Bui Xuan Hai 《Journal of Mathematical Sciences》1997,83(5):617-625
For any (noncommutative) skew field T, the lattice of subgroups of the special linear group Λ=SL(n,T) that contain the subgroup
Δ=SD(n,T) of diagonal matrices (with Dieudonné determinants equal to 1) is studied. It is established that for any subgroup
H, Δ≤H≤Λ, there exists a uniquely determined unital net σ such that Λ(σ)≤H≤N(σ), where Λ(σ) is the net subgroup associated
with the net σ and N(σ) is its normalizer in Λ. Bibliography: 11 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 91–103.
Translated by Bui Xuan Hai. 相似文献
11.
P. V. Semenov 《Mathematical Notes》1999,65(2):214-220
Theorems on the local extendability of selections for non-convex-valued maps of paracompact spaces into Banach spaces, i.e.,
infinite-dimensional analogs of the finite-dimensional Michael selection theorem are proved. We were able to obtain these
results under an appropriate metric control of the local degree of nonconvexity on the valuesF(x), which naturally leads us to introduce the notion of equi-locally paraconvex families of sets. It is shown that all convex
subsets of the integral curves of the differential equationy′=f(x,y) with a continuous right-hand sidef and the isometric images of such subsets form an equi-locally paraconvex family of subsets of a Euclidean space.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 261–269, February, 1999. 相似文献
12.
P. M. Akhmet’ev 《Journal of Mathematical Sciences》2009,159(6):753-760
In this paper, a geometric approach to stable homotopy groups of spheres based on the Pontryagin–Thom construction is proposed.
From this approach, a new proof of the Hopf-invariant-one theorem of J. F. Adams for all dimensions except 15, 31, 63, and
127 is obtained. It is proved that for n > 127, in the stable homotopy group of spheres Π
n
, there is no element with Hopf invariant one. The new proof is based on geometric topology methods. The Pontryagin–Thom theorem
(in the form proposed by R. Wells) about the representation of stable homotopy groups of the real, projective, infinite-dimensional
space (these groups are mapped onto 2-components of stable homotopy groups of spheres by the Kahn–Priddy theorem) by cobordism
classes of immersions of codimension 1 of closed manifolds (generally speaking, nonoriented) is considered. The Hopf invariant
is expressed as a characteristic class of the dihedral group for the self-intersection manifold of an immersed codimension-1
manifold that represents the given element in the stable homotopy group. In the new proof, the geometric control principle
(by M. Gromov) for immersions in the given regular homotopy classes based on the Smale–Hirsch immersion theorem is required.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 3–15, 2007. 相似文献
13.
Antonio Boccuto Xenofon Dimitriou Nikolaos Papanastassiou 《Central European Journal of Mathematics》2011,9(6):1298-1311
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results. 相似文献
14.
We present conditions under which the subdifferential of a proper convex lower-semicontinuous functional in a Fréchet space
is a bounded upper-semicontinuous mapping. The theorem on the boundedness of a subdifferential is also new for Banach spaces.
We prove a generalized Weierstrass theorem in Fréchet spaces and study a variational inequality with a set-valued mapping.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1385–1394, October, 2005. 相似文献
15.
We investigate the compactness of one class of bounded subsets in Banach and locally convex spaces. We obtain a generalization
of the Banach-Alaoglu theorem to a class of subsets that are not polars of convex balanced neighborhoods of zero.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp 731–739, June. 2000. 相似文献
16.
Beloslav Riečan 《Mathematica Slovaca》2010,60(5):655-664
The classical Poincaré strong recurrence theorem states that for any probability space (Ω, ℒ, P), any P-measure preserving transformation T, and any A ∈ ℒ, almost all points of A return to A infinitely many times. In the present paper the Poincaré theorem is proved when the σ-algebra ℒ is substituted by an MV-algebra of a special type. Another approach is used in [RIEČAN, B.: Poincaré recurrence theorem in MV-algebras. In: Proc. IFSA-EUSFLAT 2009 (To appear)], where the weak variant of the theorem is proved, of course, for arbitrary MV-algebras.
Such generalizations were already done in the literature, e.g. for quantum logic, see [DVUREČENSKIJ, A.: On some properties of transformations of a logic, Math. Slovaca 26 (1976), 131–137. 相似文献
17.
Fabien Trihan 《manuscripta mathematica》1998,96(4):397-419
The purpose of this article is to give a cohomological formula for the unit-root part of the L-function associated to a Barsotti-Tate group G on a scheme S over a field of characteristic p when G extends to some compactification of S. This is an analogue of a part of a conjecture of Katz according to wich the L-function of an F-crystal should be expressed in terms of the p-adic etale sheaf corresponding to the unit-root part of the crystal. In order to carry out this project, we use the technics
of [E-LS II] wich require in our case an extension of the Dieudonné crystalline theory ([B-B-M]) to “crystal of level mG” in the sense of Berthelot. We show that the unit-root L-function of the Dieudonné crystal associated to G can be expressed in terms of the syntomic cohomology of the Ext group of G by the constant sheaf.
Received: 24 March 1997 / Revised version: 6 January 1998 相似文献
18.
M. I. Gordin 《Journal of Mathematical Sciences》1998,88(1):7-12
Let T be a measure-preserving transformation of a probability space (X, F, μ) and let A be the generator of a μ-symmetric
Markov process with state space X. Under the assumption that A is an “eigenvector” for T an extension of T is constructed
in terms of A. By means of this extension a version of the central limit theorem is proved via approximation by martingales.
Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 10–19.
Translated by V. Sudakov. 相似文献
19.
《Quaestiones Mathematicae》2013,36(3-4):303-309
Abstract For a completely regular space X and a normed space E let Ck (x, E) (resp., Cp (x, E)) be the set of all E-valued continuous maps on X endowed with the compact-open (resp., pointwise convergence) topology. It is shown that the set of all F-valued linear continuous maps on Ck (x, E) when equipped with the topology of uniform convergence on the members of some families of bounded subsets of Ck (x, E) is a complete uniform space if F is a Band space and X is Dieudonné complete. This result is applied to prove that Dieudonné completeness is preserved by linear quotient surjections from Ck (x, E) onto Ck (Y, E) (resp., from Cp (x, E) onto Cp (x, E)) provided E, F are Band spaces and Y is a k-space. 相似文献
20.
Giuseppe Di Maio Enrico Meccariello Somashekhar A. Naimpally 《Mediterranean Journal of Mathematics》2006,3(2):189-204
In this paper we use Bartle’s technique to study duality between a topological space and a function space. Normally such a
duality forms an essential part of Functional Analysis. We introduce several new topologies such as the topology of even convergence Te, the closed-cocompact topology Tk ′, the (strong) local proximal convergence.
We explore the topological groups of self-homeomorphisms of a topological space and shed light on the earlier work of Arens,
Dieudonné, Di Concilio. We also study the concepts such as evenly equidistant, functionally equicontinuous, due to Bouziad-Troallic
and topologically equicontinuous due to Royden.
In memory of Professor Enrico Meccariello who made a considerable contribution to this work and who suddenly passed away before
his time 相似文献