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1.
Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. Suppose that L is finite and that any noncommutative division algebra appearing as a simple component in the Wedderburn decomposition of Q
L is the classical Cayley–Dickson algebra over Q. Then the unit loop of the alternative loop ring Z
L of L over the ring of rational integers is finitely generated. 相似文献
2.
It is observed that the additive as well as multiplicative Jordan decompositions hold in alternative loop algebras of finiteRA loops and theRA loops for which the additive Jordan decomposition holds in the integral loop ring are characterized. Multiplicative Jordan
decomposition (MJD) inZL, whereL is a finiteRA loop with cyclic centre is analysed, besides settling MJD for integral loop rings of allRA loops of order ≤32. It is also shown that for any finiteRA loopL,U
(ZL) is an almost splittable Moufang loop.
Research of the second author is supported by CSIR. 相似文献
3.
Peter Frankl 《Combinatorica》1984,4(2-3):141-148
LetX be a finite set ofn elements and ℓ a family ofk-subsets ofX. Suppose that for a given setL of non-negative integers all the pairwise intersections of members of ℓ have cardinality belonging toL. Letm(n, k, L) denote the maximum possible cardinality of ℓ. This function was investigated by many authors, but to determine its exact
value or even its correct order of magnitude appears to be hopeless. In this paper we investigate the case |L|=3. We give necessary and sufficient conditions form(n, k, L)=O(n) andm(n, k, L)≧O(n
2), and show that in some casesm(n, k, L)=O(n
3/2), which is quite surprising. 相似文献
4.
Let L/K be an ℓ-cyclic extension with Galois group G of algebraic function fields over an algebraically closed field k of characteristic p ≠ ℓ. In this paper, the -module structure of the ℓ-torsion of the Jacobian associated to L is explicitly determined. 相似文献
5.
A submeasure μ defined on the subsets of is nonatomic if for every ℓ ≥ 1 there exists a partition of into a finite number of parts on which μ is bounded from above by 1/ℓ. In this paper we answer several natural questions concerning nonatomic submeasures d
F
that are determined (like the standard density) by a family F of finite subsets of . We first show that if the number of n-element sets in F grows at most exponentially with n, then d
F
is nonatomic; but if this growth condition fails, then d
F
need not be nonatomic in general. We next prove that, for a nonatomic submeasure d
F
, the minimal number of sets in a 1/ℓ-small partition of can grow arbitrarily fast with ℓ. We also give a simple example of a nonatomic submeasure that is not equivalent to a submeasure of type d
F
.
The second author acknowledges a generous support of the Foundation for Polish Science. 相似文献
6.
T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1999,109(1):75-85
For 1 ≤p ≤ ∞ we show that there are no denting points in the unit ball of ℓ(lp). This extends a result recently proved by Grząślewicz and Scherwentke whenp = 2 [GS1]. We also show that for any Banach spaceX and for any measure space (Ω, A, μ), the unit ball of ℓ(L
1 (μ), X) has denting points iffL
1(μ) is finite dimensional and the unit ball ofX has a denting point. We also exhibit other classes of Banach spacesX andY for which the unit ball of ℓ(X, Y) has no denting points. When X* has the extreme point intersection property, we show that all ‘nice’ operators in the unit
ball of ℓ(X, Y) are strongly extreme points. 相似文献
7.
Wolfgang Arendt 《Positivity》2008,12(1):25-44
Extending results of Davies and of Keicher on ℓp we show that the peripheral point spectrum of the generator of a positive bounded C0-semigroup of kernel operators on Lp is reduced to 0. It is shown that this implies convergence to an equilibrium if the semigroup is also irreducible and the
fixed space non-trivial. The results are applied to elliptic operators.
Dedicated to the memory of H.H. Schaefer 相似文献
8.
Jorge Martínez 《Czechoslovak Mathematical Journal》2006,56(2):437-474
In an algebraic frame L the dimension, dim(L), is defined, as in classical ideal theory, to be the maximum of the lengths n of chains of primes p
0 < p
1 < ... < p
n
, if such a maximum exists, and ∞ otherwise. A notion of “dominance” is then defined among the compact elements of L, which affords one a primefree way to compute dimension.
Various subordinate dimensions are considered on a number of frame quotients of L, including the frames dL and zL of d-elements and z-elements, respectively. The more concrete illustrations regarding the frame convex ℓ-subgroups of a lattice-ordered group
and its various natural frame quotients occupy the second half of this exposition.
For example, it is shown that if A is a commutative semiprime f-ring with finite ℓ-dimension then A must be hyperarchimedean. The d-dimension of an ℓ-group is invariant under formation of direct products, whereas ℓ-dimension is not. r-dimension of a commutative semiprime f-ring is either 0 or infinite, but this fails if nilpotent elements are present. sp-dimension coincides with classical Krull dimension in commutative semiprime f-rings with bounded inversion. 相似文献
9.
This paper deals with a reducible sℓ(2,C) action on the formal power series ring. The purpose of this paper is to confirm a special case of the Yau conjecture:
Suppose that sℓ(2,C) acts on the formal power series ring via (1.1). Then I(f) = (ℓ
i1) ⊕ (ℓ
i2) ⊕... ⊕ (ℓ
is
) modulo some one dimensional sℓ(2,C) representations where (ℓ
i
) is an irreducible sℓ(2,C) representation of ℓ
i
dimension and {ℓ
i1
ℓ
i2,...,ℓ
is
} ⊆ {ℓ
1
, ℓ
2...,ℓ
r
}. Unlike classical invariant theory which deals only with irreducible action and 1-dimensional representations, we treat
the reducible action and higher dimensional representations successively. 相似文献
10.
Zoltán Füredi 《Combinatorica》1984,4(2-3):161-168
Let ℓ be a set-system ofr-element subsets on ann-element set,r≧3. It is proved that if |ℓ|>3.5
then ℓ contains four distinct membersA, B, C, D such thatA∪B=C∪D andA∩B=C∩D=0. 相似文献
11.
Let φ be an Orlicz function that has a complementary function φ* and let ℓφ be an Orlicz sequence space. We prove two results in this paper. Result 1:
, the Fremlin projective tensor product of ℓφ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓφ and X have the Radon-Nikodym property. Result 2:
, the Wittstock injective tensor product of ℓφ with a Banach lattice X, has the Radon-Nikodym property if and only if both ℓφ and X have the Radon-Nikodym property and each positive continuous linear operator from hφ* to X is compact.
We dedicate this paper to the memory of H. H. Schaefer
The first-named author gratefully acknowledges support from the Faculty Research Program of the University of Mississippi
in summer 2004. 相似文献
12.
We study hypercyclicity and supercyclicity of weighted shifts on ℓ∞, with respect to the weak * topology. We show that there exist bilateral shifts that are weak * hypercyclic but fail to be
weak * sequentially hypercyclic. In the unilateral case, a shift T is weak * hypercyclic if and only if it is weak * sequentially hypercyclic, and this is equivalent to T being either norm, weak, or weak-sequentially hypercyclic on c0 or ℓp (1 ≤ p < ∞). We also show that the set of weak * hypercyclic vectors of any unilateral or bilateral shift on ℓ∞ is norm nowhere dense. Finally, we show that ℓ∞ supports an isometry that is weak * sequentially supercyclic. 相似文献
13.
Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. 相似文献
14.
Henk Bruin Juan Rivera-Letelier Weixiao Shen Sebastian van Strien 《Inventiones Mathematicae》2008,172(3):509-533
In this paper, we study the dynamics of a smooth multimodal interval map f with non-flat critical points and all periodic
points hyperbolic repelling. Assuming that |Dfn(f(c))|→∞ as n→∞ holds for all critical points c, we show that f satisfies the so-called backward contracting property with
an arbitrarily large constant, and that f has an invariant probability μ which is absolutely continuous with respect to Lebesgue
measure and the density of μ belongs to Lp for all p<ℓmax/(ℓmax-1), where ℓmax denotes the maximal critical order of f. In the appendix, we prove that various growth conditions on the derivatives along
the critical orbits imply stronger backward contraction. 相似文献
15.
Intersection theorems with geometric consequences 总被引:3,自引:0,他引:3
In this paper we prove that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℱ we have |F ∩F′| ≡ μi (modp) for somei, 1 ≦i≦s, then |ℱ|≦(
s
n
).
As a consequence we show that ifR
n
is covered bym sets withm<(1+o(1)) (1.2)
n
then there is one set within which all the distances are realised.
It is left open whether the same conclusion holds for compositep. 相似文献
16.
Ferenc Weisz 《数学学报(英文版)》2010,26(9):1627-1640
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, e∞) to W(Lp,e∞). This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W(L1, e∞) velong to L1. 相似文献
17.
Elena Zizioli 《Results in Mathematics》2008,51(3-4):373-382
Starting from two loops (H, +) and (K, ·), a new loop L can be defined by means of a suitable map Θ : K → Sym H (cf. [3]). Such a loop is called semidirect product of H and K with respect to Θ and denoted by H ×Θ
K =: L. Here we consider the class of those semidirect products in which Θ : K → Aut(H, +) is a homomorphism, this situation being quite akin to the group case.
Some relevant algebraic properties of the loop L (Bol condition, Moufang etc.) can be inherited from H and K.
In the case that K is a group we investigate the possibility of describing L by a partition (or fibration). In this way we propose a generalization of [8] for the non associative case.
Received: September 20, 2007. Revised: November 8, 2007. 相似文献
18.
Laurent Miclo 《Probability Theory and Related Fields》1999,114(4):431-485
Let G be a finite and connected graph, we will note by l(G) the maximum length of an injective path in G. We will show (by two dictinct proofs, one using sub-trees of G and the other based on multiflows of paths) that sup
(P,μ)∈?(G)
I(P, μ)/λ(P, μ) = l(G), where the supremum is taken over all Markovian kernels P reversible with respect to a probability μ and whose allowed transitions are given by the edges of G, and where I(P, μ) (respectively λ(P, μ)) is the isoperimetric constant (resp. the spectral gap) associated to the couple (P, μ). Then we will study more precisely the same supremum, but where the probability μ is also fixed. These results give optimal
minorations of the spectral gap which are linear with respect to the isoperimetric constant (and not quadratic, as in the
Cheeger inequality), and we will give several examples on infinite graphs.
Re?u: 12 ao?t 1997 / Version révisée: 9 novembre 1998 相似文献
19.
Francisco L. Hernández Baltasar Rodriguez-Salinas 《Israel Journal of Mathematics》1998,104(1):191-220
We study the setP
X
of scalarsp such thatL
p
is lattice-isomorphically embedded into a given rearrangement invariant (r.i.) function spaceX[0, 1]. Given 0<α≤β<∞, we construct a family of Orlicz function spacesX=L
F
[0, 1], with Boyd indicesα andβ, whose associated setsP
X
are the closed intervals [γ, β], for everyγ withα≤γ≤β. In particular forα>2, this proves the existence of separable 2-convex r.i. function spaces on [0,1] containing isomorphically scales ofL
p
-spaces for different values ofp. We also show that, in general, the associated setP
X
is not closed. Similar questions in the setting of Banach spaces with uncountable symmetric basis are also considered. Thus,
we construct a family of Orlicz spaces ℓ
F
(I), with symmetric basis and indices fixed in advance, containing ℓ
p
(Γ-subspaces for differentp’s and uncountable Λ⊂I. In contrast with the behavior in the countable case (Lindenstrauss and Tzafriri [L-T1]), we show that the set of scalarsp for which ℓ
p
(Γ) is isomorphic to a subspace of a given Orlicz space ℓ
F
(I) is not in general closed.
Supported in part by DGICYT grant PB 94-0243. 相似文献
20.
If A⊂ L0(X, μ) is a convex solid subset of L0(X, μ), then there exist disjoint X0 and X1 with X = X0∪ X1 such that A| X_0 is dense in L0(X0, μ) and A|X_1 is bounded in measure in L0(X1, μ). 相似文献