共查询到20条相似文献,搜索用时 78 毫秒
1.
Edmond E. Granirer 《Israel Journal of Mathematics》1990,69(3):321-336
LetG ⊂ Aut ℳ be a countable group, ℳ a Von Neumann algebra. LetE be a set of pure states on ℳ such thatG*E ⊂E, S
G be the set ofG invariant states on ℳ andS
E
G
=S
G ∩w* cl coE. We investigate in this paper some geometric properties for the setS
E
G
which turn out to be equivalent to amenability for the groupG. For example, we show thatS
E
G
⊂ ℳ* (S
E
G
has the WRNP) implies that ℳ contains minimal projections (ê containsfinite G invariant orbits) hold true, for all ℳ iffG is amenable. Furthermore we show that ifG is amenable thenS
G ∩M
*
⊥
contains a big set, thus improving results obtained by Ching Chou in [2]. These results imply that no action of an amenable
countable groupG on an arbitraryW* algebra ℳ iss — strongly ergodic. Moreover cardS
G ∩M
*
⊥
≧2
c
(see M. Choda [4], K. Schmidt [21] and compare with A. Connes and B. Weiss [5]).
The author gratefully acknowledges the support of an Izaak Walton Killam Memorial Senior Fellowship. 相似文献
2.
S. P. Ponomarev 《Mathematical Notes》1995,58(3):960-965
A functionf∶G→ℝ
n
, whereG is an open set in ℝ
n
, has theN
−1-property if for allE⊂ℝ
n
we have {|E|=0⇒|f
−1(E)|=0} (|·| is the Lebesgue measure). The article is concerned with the relations between theN
−1-property of functions, the maximal rank of derivatives, and the differentiability almost everywhere of composite functions.
Translated fromMatematicheskie Zametki, Vol. 58. No. 3, pp. 411–418, September, 1995. 相似文献
3.
Raffaele Mosca 《Graphs and Combinatorics》2001,17(3):517-528
Let G be a graph with n vertices, and denote as γ(G) (as θ(G)) the cardinality of a minimum edge cover (of a minimum clique cover) of G. Let E (let C) be the edge-vertex (the clique-vertex) incidence matrix of G; write then P(E)={x∈ℜ
n
:Ex≤1,x≥0}, P(C)={x∈ℜ
n
:Cx≤1,x≥0}, α
E
(G)=max{1
T
x subject to x∈P(E)}, and α
C
(G)= max{1
T
x subject to x∈P(C)}. In this paper we prove that if α
E
(G)=α
C
(G), then γ(G)=θ(G).
Received: May 20, 1998?Final version received: April 12, 1999 相似文献
4.
Gordan Savin 《Israel Journal of Mathematics》1992,80(1-2):195-205
LetG andH ⊂G be two real semisimple groups defined overQ. Assume thatH is the group of points fixed by an involution ofG. Letπ ⊂L
2(H\G) be an irreducible representation ofG and letf επ be aK-finite function. Let Γ be an arithmetic subgroup ofG. The Poincaré seriesP
f(g)=ΣH∩ΓΓ
f(γ{}itg) is an automorphic form on Γ\G. We show thatP
f is cuspidal in some cases, whenH ∩Γ\H is compact.
Partially supported by NSF Grant # DMS 9103608. 相似文献
5.
Under appropriate conditions on Abelian topological groups G and H, an orthogonality ⊥ ⊂ G
2 and a σ-algebra of subsets of G we decompose an -measurable function f: G → H which is orthogonally additive modulo a discrete subgroup K of H into its continuous additive and continuous quadratic part (modulo K).
Research supported by the Silesian University Mathematics Department (Functional Equations on Abstract Structures program
— the first author, and Iterative Functional Equations and Real Analysis program — the second author). 相似文献
6.
Y. Katznelson 《Israel Journal of Mathematics》1979,33(1):1-4
A closed setE⊂T is an αβ-set, where α and β are elements of infinite order inT ifE⊂E−α). ∪ (E−β). We give two constructions of “thin” αβ-sets. 相似文献
7.
Parviz Ahmadi 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):174-177
The paper studies closed Lie subgroups G ⊂ Iso(ℝ
n
) acting by cohomogeneity one on ℝ
n
and prove that when there is no singular orbit, then there is a simply connected, solvable and closed Lie subgroup F ⊂ G which acts by cohomogeneity one on ℝ
n
and the two actions are orbit equivalent. 相似文献
8.
We define and study a class of summable processes, called additive summable processes, that is larger than the class used
by Dinculeanu and Brooks [D-B].
We relax the definition of a summable processesX:Ω×ℝ+→E⊂L(F, G) by asking for the associated measureI
X to have just an additive extension to the predictableσ-algebra ℘, such that each of the measures (I
X)
z
, forz∈(L
G
p
)*, beingσ-additive, rather than having aσ-additive extension. We define a stochastic integral with respect to such a process and we prove several properties of the
integral. After that we show that this class of summable processes contains all processesX:Ω×ℝ+→E⊂L(F, G) with integrable semivariation ifc
0 ∋G. 相似文献
9.
10.
Fabrice Krieger 《Israel Journal of Mathematics》2009,172(1):425-444
Let G be a countable amenable group and P a polyhedron. The mean topological dimension mdim(X,G) of a subshift X ⊂ P
G
is a real number satisfying 0 ≤ mdim(X,G) ≤ dim(P), where dim(P) denotes the usual topological dimension of P. We give a construction of minimal subshifts X ⊂ P
G
with mean topological dimension arbitrarily close to dim(P). 相似文献
11.
Wolfgang Lück 《Inventiones Mathematicae》2002,149(1):123-152
We prove a version of the L
2-index Theorem of Atiyah, which uses the universal center-valued trace instead of the standard trace. We construct for G-equivariant K-homology an equivariant Chern character, which is an isomorphism and lives over the ring ℤ⊂λ
G
⊂ℚ obtained from the integers by inverting the orders of all finite subgroups of G. We use these two results to show that the Baum-Connes Conjecture implies the modified Trace Conjecture, which says that
the image of the standard trace K
0(C
*
r
(G))→ℝ takes values in λ
G
. The original Trace Conjecture predicted that its image lies in the additive subgroup of ℝ generated by the inverses of all
the orders of the finite subgroups of G, and has been disproved by Roy [15].
Oblatum 10-IV-2001 & 18-X-2001?Published online: 15 April 2002 相似文献
12.
Ved Prakash Gupta 《Proceedings Mathematical Sciences》2008,118(4):583-612
We give an identification between the planar algebra of the subgroupsubfactor R ⋊ H ⊂ R ⋊ G and the G-invariant planar subalgebra of the planar algebra of the bipartite graph ★
n
, where n = [G: H]. The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of
the standard invariant of R ⋊ H ⊂ R ⋊ G in terms of operator matrices.
We also obtain an identification between the planar algebra of the fixed algebra subfactor R
G
⊂ R
H
and the G-invariant planar subalgebra of the planar algebra of the ‘flip’ of ★
n
. 相似文献
13.
A N Starkov 《Proceedings Mathematical Sciences》1994,104(3):495-514
The paper concerns rigidity problem for lattices in simply connected solvable Lie groups. A lattice Γ⊂G is said to be rigid if for any isomorphism ϕ:Γ→Γ′ with another lattice Γ′⊂G there exists an automorphism
which extends ϕ. An effective rigidity criterion is proved which generalizes well-known rigidity theorems due to Malcev and
Saito. New examples of rigid and nonrigid lattices are constructed. In particular, we construct: a) rigid lattice Γ⊂G which is not Zariski dense in the adjoint representation ofG, b) Zariski dense lattice Γ⊂G which is not rigid, c) rigid virtually nilpotent lattice Γ in a solvable nonnilpotent Lie groupG. 相似文献
14.
M. A. Turmanov 《Journal of Mathematical Sciences》2006,137(6):5336-5345
Torsion-free Abelian groups G and H are called quasi-equal (G ≈ H) if λG ⊂ H ⊂ G for a certain natural number ≈. It is known (see [3]) that the quasi-equality of torsion-free Abelian groups can be represented
as the equality in an appropriate factor category. Thus while dealing with certain group properties it is usual to prove that
the property under consideration is preserved under the transition to a quasi-equal group. This trick is especially frequently
used when the author investigates module properties of Abelian groups; here a group is considered as a left module over its
endomorphism ring. On the other hand, a topical problem in the Abelian group theory is the problem of investigation of pureness
in the category of Abelian groups (see [4]). We consider the pureness introduced by P. Cohn [2] for Abelian groups as modules
over their endomorphism rings. Particularity of the investigation of the properties of pureness for the Abelian group G as the module
E
(G)G lies in the fact that this is a more general situation than the investigation of pureness for a unitary module over an arbitrary
ring R with the identity element. Indeed, if
R
M is an arbitrary unitary left module and M
+ is its Abelian group, then each element from R can be identified with an appropriate endomorphism from the ring E(M
+) under the canonical ring homomorphism R → E(M
+). Then it holds that if
E(M+)
N is a pure submodule in
E(M+)
M
+, then
R
N is a pure submodule in
R
M. In the present paper the interrelations between pureness, servantness, and quasi-decompositions for Abelian torsion-free
groups of finite rank will be investigated.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 2, pp. 225–238,
2004. 相似文献
15.
Denis A. Labutin 《manuscripta mathematica》2000,102(2):163-167
We show that any set E⊂C
n
, n≥ 2, with finite Hausdorff measure? is pluripolar. The result is sharp with respect to the measuring function. The new idea in the proof is to combine a construction
from potential theory, related to the real variational integral , , with properties of the pluricomplex relative extremal function for the Bedford–Taylor capacity.
Received: 20 May 1999 相似文献
16.
L. Barchini 《Mathematische Annalen》2003,326(2):331-346
Let G be a connected semisimple Lie group contained in its simply connected complexification G
C
. Let KG∩K
C
be a maximal compact subgroup of G. Denote by X
o
the unique closed G-orbit in the full flag manifold ℱ and by 𝒪 the unique open K
C
-orbit in ℱ. The set consisting of the elements gK
C
so that gX
o
⊂𝒪 is an Stein extension of G/K⊂G
C
/K
C
. There is a universal domain , natural form the point of view of group actions which has been conjectured to be Stein. The main result of this paper is
the inclusion . In the second part of the paper I show, under some dominance condition in the parameter, that representations in Dolbeault
cohomology can be realized as holomorphic sections of vector bundles over .
Received: 9 September 2002 / Revised version: 12 July 2002 /
Published online: 8 April 2003
Mathematics Subject Classification (2002): 22E30
Research partially supported by NSF grant DMS-9801605 and DMS 0074991. 相似文献
17.
A. N. Starkov 《Mathematical Notes》1995,58(1):744-751
Ergodic one-parameter flows (G/Γ,g
ℝ) induced by the left action of a subgroupg
ℝ ⊂G on homogeneous spaces of finite volume are considered. Letℳ ⊂ ℝ+ be the set of allt>0 such that the cascade (G/Γ,g
t
ℤ) is metrically isomorphic to the cascade (G/Γ,g
ℤ). We prove that eitherℳ is at most countable or the subgroupg
ℝ is horocyclic andℳ=ℝ+. We prove that a metric isomorphism of ergodic quasi-unipotent cascades (or flows) is affine on almost all fibers of a certain
natural bundle. The result generalizes Witte's theorem on the affinity of such isomorphisms of cascades with the mixing property;
this is applied to the study of the structure of the setℳ ⊂ ℝ+. The proof is based on the fundamental Ratner theorem stating that the ergodic measures of unipotent cascades are algebraic.
Translated fromMatematicheskie Zametki, Vol. 58, No. 1, pp. 98–110, July, 1995.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 94-01-00082a and by the
International Science Foundation. 相似文献
18.
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
19.
Imre Patyi 《Mathematische Annalen》2003,326(3):443-458
Let X be one of the Banach spaces c
0
, ℓ
p
, 1≤p<∞; Ω⊂X pseudoconvex open, a holomorphic Banach vector bundle with a Banach Lie group G
*
for structure group. We show that a suitable Runge-type approximation hypothesis on X, G
*
(which we also prove for G
*
a solvable Lie group) implies the vanishing of the sheaf cohomology groups H
q
(Ω, 𝒪
E
), q≥1, with coefficients in the sheaf of germs of holomorphic sections of E. Further, letting 𝒪Γ (𝒞Γ) be the sheaf of germs of holomorphic (continuous) sections of a Banach Lie group bundle Γ→Ω with Banach Lie groups G, G
*
for fiber group and structure group, we show that a suitable Runge-type approximation hypothesis on X, G, G
*
(which we prove again for G, G
*
solvable Lie groups) implies the injectivity (and for X=ℓ1 also the surjectivity) of the Grauert–Oka map H
1
(Ω, 𝒪Γ)→H
1
(Ω, 𝒞Γ) of multiplicative cohomology sets.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L20, 32L05, 46G20
RID="*"
ID="*" Kedves Laci Móhan kisfiamnak.
RID="*"
ID="*" To my dear little Son 相似文献
20.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
X ? *\Bbb CX \rightarrow {}{^{\ast}{\Bbb C}}
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
Mw(X)/M0(X){\cal M}_{\omega}(X)/{\cal M}_0(X)
, for certain external subspaces
M0(X), Mw(X){\cal M}_0(X), {\cal M}_{\omega}(X)
of the hyperfinite dimensional Banach space
*\Bbb CX{}{^{\ast}{\Bbb C}}^X
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
Mw(G)/M0(G){\cal M}_{\omega}(G)/{\cal M}_0(G)
are isometrically isomorphic as Banach algebras. 相似文献