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1.
LetT: X→X be a deterministic dynamical system preserving a probability measure μ. A dynamical Borel-Cantelli lemma asserts that for
certain sequences of subsetsA
n
⊃ X and μ-almost every pointx∈X the inclusionT
n
x∈A
n
holds for infinitely manyn. We discuss here systems which are either symbolic (topological) Markov chain or Anosov diffeomorphisms preserving Gibbs
measures. We find sufficient conditions on sequences of cylinders and rectangles, respectively, that ensure the dynamical
Borel-Cantelli lemma.
Partially supported by NSF grant DMS-9732728.
Partially supported by NSF grant DMS-9704489. 相似文献
2.
Paul Trow 《Israel Journal of Mathematics》1990,71(2):229-238
Iff: Σ
A
→ Σ
A
is an endomorphism of an irreducible shift of finite type, andp is a rational prime which divides the degree off, thenp divides every non-leading coefficient of χA. We also give constraints on the possible degrees of finite-to-one factor maps between shifts of finite type. 相似文献
3.
Hannah Alpert 《Archiv der Mathematik》2011,96(4):311-320
Let A be an infinite set that generates a group G. The sphere S
A
(r) is the set of elements of G for which the word length with respect to A is exactly r. We say G admits all finite transitions if for every r ≥ 2 and every finite symmetric subset W ì G\{e}{W \subset G{\setminus}\{e\}}, there exists an A with S
A
(r) = W. In this paper we determine which countable abelian groups admit all finite transitions. We also show that
\mathbbRn{\mathbb{R}^n} and the finitary symmetric group on
\mathbbN{\mathbb{N}} admit all finite transitions. 相似文献
4.
We show that if A is a Hilbert–space operator, then the set of all projections onto hyperinvariant subspaces of A, which is contained in the von Neumann algebra υN(A) that is generated by A, is independent of the representation of υ N(A), thought of as an abstract W*–algebra. We modify a technique of Foias, Ko, Jung and Pearcy to get a method for finding nontrivial hyperinvariant subspaces
of certain operators in finite von Neumann algebras. We introduce the B–circular operators as a special case of Speicher's B–Gaussian operators in free probability theory, and we prove several results about a B–circular operator z, including formulas for the B–valued Cauchy– and R–transforms of z*z. We show that a large class of L∞([0,1])–circular operators in finite von Neumann algebras have nontrivial hyperinvariant subspaces, and that another large
class of them can be embedded in the free group factor L(F3). These results generalize some of what is known about the quasinilpotent DT–operator.
Supported in part by NSF Grant DMS-0300336.
with an Appendix by Gabriel Tucci 相似文献
5.
The Kirillov–Reshetikhin modules Wr,s are finite-dimensional representations of quantum affine algebras U’q labeled by a Dynkin node r of the affine Kac–Moody algebra
and a positive integer s. In this paper we study the combinatorial structure of the crystal basis B2,s corresponding to W2,s for the algebra of type D(1)n.
2000 Mathematics Subject Classification Primary—17B37; Secondary—81R10
Supported in part by the NSF grants DMS-0135345 and DMS-0200774. 相似文献
6.
To every von Neumann algebra, one can associate a (multiplicative) determinant defined on the invertible elements of the algebra with range a subgroup of the Abelian group of the invertible elements of the center of the von Neumann algebra. This determinant is a normalization of the usual determinant for finite von Neumann algebras of type I, for the type II1-case it is the Fuglede-Kadison determinant, and for properly infinite von Neumann algebras the determinant is constant equal to 1. It is proved that every invertible element of determinant 1 is a product of a finite number of commutators. This extends a result of T. Fack and P. de la Harpe for II1-factors. As a corollary, it follows that the determinant induces an injection from the algebraicK
1-group of the von Neumann algebra into the Abelian group of the invertible elements of the center. Its image is described. Another group,K
1
w
(A), which is generated by elements in matrix algebras overA that induce injective right multiplication maps, is also computed. We use the Fuglede-Kadison determinant to detect elements in the Whitehead group Wh(G).Partially supported by NSF Grant DMS-9103327. 相似文献
7.
Sébastien Ferenczi 《Israel Journal of Mathematics》1982,42(4):334-342
Ergodic theory: for every dynamical system (X,A,T, μ), totally ergodic and of finite entropy, there exist a sequenceS of integers, of upper density zero, and a partitionQ ofX, such that V
i∈S
T
−i Q is the whole σ-algebraA. Furthermore, there is a “universal” sequenceS
0 for which this property is true if we restrict ourselves to the class of strongly mixing systems.
相似文献
8.
V. M. Manuilov 《Mathematical Notes》1997,62(6):726-730
The classical Hilbert-Schmidt theorem can be extended to compact operators on HilbertA-modules overW
*-algebras of finite type; i.e., with minor restrictions, compact operators onH*
A
can be diagonalized overA. We show that ifB is a weakly denseC
*-subalgebra ofA with real rank zero and if some additional condition holds, then the natural extension fromH
B
toH*
A
⊃H
B
of a compact operator can be diagonalized so that the diagonal elements belong to the originalC
*-algebraB.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 865–870, December, 1997.
Translated by O. V. Sipacheva 相似文献
9.
For a finite triangulation of the plane with faces properly coloured white and black, let
AW\mathcal{A}_{W}
be the abelian group constructed by labelling the vertices with commuting indeterminates and adding relations which say that
the labels around each white triangle add to the identity. We show that
AW\mathcal{A}_{W}
has free rank exactly two. Let
AW*\mathcal{A}_{W}^{*}
be the torsion subgroup of
AW\mathcal{A}_{W}
, and
AB*\mathcal{A}_{B}^{*}
the corresponding group for the black triangles. We show that
AW*\mathcal{A}_{W}^{*}
and
AB*\mathcal{A}_{B}^{*}
have the same order, and conjecture that they are isomorphic.
For each spherical latin trade W, we show there is a unique disjoint mate B such that (W,B) is a connected and separated bitrade. The bitrade (W,B) is associated with a two-colourable planar triangulation and we show that W can be embedded in
AW*\mathcal{A}_{W}^{*}
, thereby proving a conjecture due to Cavenagh and Drápal. The proof involves constructing a (0,1) presentation matrix whose
permanent and determinant agree up to sign. The Smith normal form of this matrix determines
AW*\mathcal{A}_{W}^{*}
, so there is an efficient algorithm to construct the embedding. Contrasting with the spherical case, for each genus g≥1 we construct a latin trade which is not embeddable in any group and another that is embeddable in a cyclic group. 相似文献
10.
A code D over Z
2
n
is called a quasi-perfect Lee distance-(2t + 1) code if d
L(V,W) ≥ 2t + 1 for every two code words V,W in D, and every word in Z
2
n
is at distance ≤ t + 1 from at least one code word, where D
L(V,W) is the Lee distance of V and W. In this paper we present a fast decoding algorithm for quasi-perfect Lee codes. The basic idea of the algorithm comes from
a geometric representation of D in the 2-dimensional plane. It turns out that to decode a word it suffices to calculate its distance to at most four code
words. 相似文献
11.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
12.
We study a class of weighted shifts W
α defined by a recursively generated sequence α ≡ α0, … , α
m−2, (α
m−1, α
m
, α
m+1)∧ and characterize the difference between quadratic hyponormality and positive quadratic hyponormality. We show that a shift
in this class is positively quadratically hyponormal if and only if it is quadratically hyponormal and satisfies a finite
number of conditions. Using this characterization, we give a new proof of [12, Theorem 4.6], that is, for m = 2, W
α is quadratically hyponormal if and only if it is positively quadratically hyponormal. Also, we give some new conditions for
quadratic hyponormality of recursively generated weighted shift W
α (m ≥ 2). Finally, we give an example to show that for m ≥ 3, a quadratically hyponormal recursively generated weighted shift W
α need not be positively quadratically hyponormal. 相似文献
13.
Tadayoshi Takebayashi 《Journal of Algebraic Combinatorics》2003,17(3):211-223
We calculate the Poincaré series of the elliptic Weyl group W(A
2
(1,1)), which is the Weyl group of the elliptic root system of type A
2
(1,1). The generators and relations of W(A
2
(1,1)) have been already given by K. Saito and the author. 相似文献
14.
Misha Feigin 《Selecta Mathematica, New Series》2012,18(1):253-281
We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals that are invariant under the action of the corresponding rational Cherednik algebra hence form
submodules in the polynomial module. We show that a quantum integrable system can be defined for every such ideal for a real
reflection group W. This leads to known and new integrable systems of Calogero–Moser type which we explicitly specify. In the case of classical
Coxeter groups, we also obtain generalized Calogero–Moser systems with added quadratic potential. 相似文献
15.
We apply subelliptic Cordes conditions and Talenti–Pucci type inequalities to prove W
2,2 and C
1,α estimates for p-harmonic functions in the Grušin plane for p near 2.J. J. Manfred; partially supported by NSF award DMS-0500983 相似文献
16.
Jack D. Koronel 《Israel Journal of Mathematics》1976,24(2):119-138
The paper gives a necessary and sufficient condition for the embedding of the Orlicz-Sobolev spaceW
kLA (Ω) inC(Ω). The same condition is also found to be necessary and sufficient so that a continuous function inW
kLA (Ω) be differentiable of orderk almost everywhere in Ω. 相似文献
17.
Paul Trow 《Israel Journal of Mathematics》1995,91(1-3):129-155
We examine the question of when a finite-to-one factor map θ: ∑A →S, from a shift of finite type onto a sofic shift, can be decomposed as a left closing map (onto a shift of finite type) followed
by a right closing map (or vice versa). We give a finite procedure for deciding this question. In general, we show that there
are finitely many such decompositions, up to conjugacy. If the degree of θ is one, then there is at most one such decomposition. 相似文献
18.
We say that A has fractional powers {A
t
}
t≥0 if there exists a nondegenerate C-regularized semigroup {W(t)}
t≥0 such that A=C
−1
W(1); then A
t
≡C
−1
W(t). We show that this generalizes the usual definition of fractional powers for nonnegative operators, and enables many operators
with spectrum containing the entire unit disc to have fractional powers. Our definition gives clear, simple proofs of the
basic properties of fractional powers. We show that, for nonnegative operators, the fractional powers with the property that,
if A is of type θ, then A
t
is of type t
θ, whenever t
θ<π, are unique. More generally, for injective G∈B(X) commuting with A, we show that an operator A of G-regularized type θ has a unique family of fractional powers with the property that A
t
is of G-regularized type t
θ whenever t
θ<π. This leads to a construction of fractional powers of operators with polynomially bounded resolvent outside of an appropriate
sector. We show that an operator is of regularized type if and only if it has exponentially bounded regularized imaginary
powers.
This work was done while the second author was visiting Ohio University, with funding from Universitat de València. He would
like to thank Ohio University and Professor deLaubenfels for their hospitality and support. 相似文献
19.
The present paper is concerned withL
p-theory of the uniformly elliptic differential operator
inR
n with coefficients of vanishing mean oscillation. Recent estimates for the Riesz transform combined with Fredholm index theory
enable us to establish invertibility of the map L:W
-1,pRn→W
1,pRn, for every 1<p<∞. As a side benefit, we obtain the existence and uniqueness theorem for the equationL
u=μ with a signed measure in the right hand side. Within the framework of quasiconformal mappings we give a fairly general
method of constructing solutions to the homogeneous equationL
u=0.
The research of the first author was supported by NSF Grant DMS-9401104. The research of the second author was carried out
during his visit to Syracuse University and was supported by NSF Grant DMS-9401104 and by GNAFA-CNR Florence. 相似文献
20.
We callE ⊆ {0,1}
k
projective if for some countableA ⊆κ there is anE
A
⊆ {0, 1}
A
such thatE=E
A
×{0,1}
k\A
andE
A
is a projective subset of the Cantor set {0, 1}
A
. We construct a model where Haar measure on {0,1}
k
has no projective lifting (and in particular no Baire lifting) for anyκ≥ω.
Research partially supported by NATO Science Fellowship. The first author would like to thank the Mathematics Department at
the University of Essex for its hospitality during the academic year 1988/89 while part of this research was being carried
out.
This research was initiated while the second author was a postdoctoral fellow at the University of Toronto. Its completion
was supported by NSF grant DMS-8505550. 相似文献