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1.
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
2.
Rolf Kultze 《manuscripta mathematica》1990,69(1):31-42
LetX be a connected, locally finite spectrum and letk(n) (n>-1) denote the (−1)-connected cover of then-th MoravaK-Theory associated to the primep.k(n) is aBP-module spectrum with π*(k(n)) ≅ ℤ
p
[υ
n
] where |v
n
| = 2(p
n
-1). We prove the following splitting theorem: Thek(n)
*-torsion ofk(n)
* (X) is already annihilated byv
n
e
(e≥1) if and only ifk(n)ΛX is homotopy equivalent to a wedge of spectrak(n) and
r
k(n) (0≤r≤e-1) where
r
k(n) denotes ther-th Postnikov factor ofk(n). Moreover we investigate splitting conditions for
r
k(n)ΛX. 相似文献
3.
LetX be a 1-connected space with Moore loop space ΩX. By a well-known theorem of J. W. Milnor and J. C. Moore [7] the Hurewicz homomorphism induces an isomorphism of Hopf algebrasU(π*(ΩX) ⊗Q)→H
*(ΩX;Q). HereU(−) denotes the universal enveloping algebra and the Lie bracket on π*(ΩX) ⊗Q is given by the Samelson product.
Assume now thatX is the geometric realization of anr-reduced simplicial set,r≥3. LetL
X
be a differential graded free Lie algebra over ℤ describing the tame homotopy type ofX according to the theory of [4]. Then the main result of the present paper is the construction of a sequence of morphisms
of differential graded algebras betwenU(L
X
) and the algebraC U
*(ΩX)z of normalized cubical chains on ΩX such that the induced morphisms on homology with coefficientsR
k
are isomorphismsH
r-1+l
(U(L
x
);R
k
) ≅H
r-1+l
C U
*(ΩX);R
k
) forl≤k; hereR
0⊆R
1⊆… is a tame ring system, i. e.R
k
)⊑Q and each primep with 2p−3≤k is invertible inR
k
.
However, it is no longer true that the Pontrjagin algebraH
≤r−1+k
(ΩX; R
k
) of ΩX in degrees ≤r−1+k is determined by π*(ΩX) or by a cofibrant (-fibrant) modelM of π*(ΩX) as will be shown by an example. But there is a filtration onH
≤r−1+k
(ΩX; R
k
) such that the associated graded algebra is isomorphic toH
≤r−1+k
(U(M); R
k
).This will be proved by using a filtered Lie algebra model ofX constructed from a bigraded model of π*(ΩX).
Supported by a CNRS grant and PROCOPE
Supported by PROCOPE 相似文献
4.
Let S⊂ℝ
k+m
be a compact semi-algebraic set defined by P
1≥0,…,P
ℓ
≥0, where P
i
∈ℝ[X
1,…,X
k
,Y
1,…,Y
m
], and deg (P
i
)≤2, 1≤i≤ℓ. Let π denote the standard projection from ℝ
k+m
onto ℝ
m
. We prove that for any q>0, the sum of the first q Betti numbers of π(S) is bounded by (k+m)
O(q
ℓ). We also present an algorithm for computing the first q Betti numbers of π(S), whose complexity is
. For fixed q and ℓ, both the bounds are polynomial in k+m.
The author was supported in part by an NSF Career Award 0133597 and a Sloan Foundation Fellowship. 相似文献
5.
Ozer TALO Feyzi BASAR 《数学学报(英文版)》2008,24(7):1205-1212
Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55(1)(2003), 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp(F) of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp(F) includes the space lp(F) and also shown that the spaces bvp(F) and lp(F) axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given. 相似文献
6.
Dominique Arlettaz 《Central European Journal of Mathematics》2004,2(1):50-56
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism
b
n
: π
n
(X)→H
n
(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π
n
(X)→E
n
(X), F
n
(X)→(E∧F)
n
(X), F
n
(X)→H
n
(X;π
0
F) and F
n
(X)→H
n+t
(X;π
t
F) for other cohomology theories E
*(−) and F
*(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in
terms of the order of the Postnikov invariants of the spectrum F. 相似文献
7.
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
8.
Michel Schreiber 《Israel Journal of Mathematics》1977,28(4):287-312
The “convex derived set” of a symmetric probability lawF on the real line is defined as the set of limits of laws ∗
j−1/k
n
F(t
j
n
η), inf 1≤j≤k
n t
j
n
→∞ ifn→∞ and the stable laws it contains are exhibited. A new criterion of stochastic compacity of the set of the powers of a probability
law is established. Finally, an isomorphism theorem between somel
p andL
0 spaces is given.
Laboratoire associé au C.N.R.S. no 224 “Processus stochastiques et applications”. 相似文献
Laboratoire associé au C.N.R.S. no 224 “Processus stochastiques et applications”. 相似文献
9.
A. Samokhin 《Transformation Groups》2010,15(1):227-242
Let X be a smooth variety over an algebraically closed field k of characteristic p, and let F: X → X be the Frobenius morphism. We prove that if X is an incidence variety (a partial flag variety in type A
n
) or a smooth quadric (in this case p is supposed to be odd) then
Hi( X,End( \sfF*OX ) ) = 0 {H^i}\left( {X,\mathcal{E}nd\left( {{\sf{F}_*}{\mathcal{O}_X}} \right)} \right) = 0 for i > 0. Using this vanishing result and the derived localization theorem for crystalline differential operators [3], we show that the Frobenius direct image
\sfF*OX {\sf{F}_*}{\mathcal{O}_X} is a tilting bundle on these varieties provided that p > h, the Coxeter number of the corresponding group. 相似文献
10.
Ke-Ang Fu 《Proceedings Mathematical Sciences》2010,120(5):611-618
Let {X
n
; n ≥ 1} be a sequence of independent and identically distributed random vectors in ℜ
p
with Euclidean norm |·|, and let X
n
(r) = X
m
if |X
m
| is the r-th maximum of {|X
k
|; k ≤ n}. Define S
n
= Σ
k≤n
X
k
and (r)
S
n
− (X
n
(1) + ... + X
n
(r)). In this paper a generalized strong invariance principle for the trimmed sums (r)
S
n
is derived. 相似文献
11.
Let K
0(Var
k
) be the Grothendieck ring of algebraic varieties over a field k. Let X, Y be two algebraic varieties over k which are piecewise isomorphic (i.e. X and Y admit finite partitions X
1, ..., X
n
, Y
1, ..., Y
n
into locally closed subvarieties such that X
i
is isomorphic to Y
i
for all i ≤ n), then [X] = [Y] in K
0(Var
k
). Larsen and Lunts ask whether the converse is true. For characteristic zero and algebraically closed field k, we answer positively this question when dim X ≤ 1 or X is a smooth connected projective surface or if X contains only finitely many rational curves. 相似文献
12.
We give sufficient conditions on Banach spaces X and Y so that their projective tensor product X ⊗π
Y, their injective tensor product X ⊗ɛ
Y, or the dual (X ⊗π
Y)* contain complemented copies of ℓp. 相似文献
13.
Dieter Bothe 《Israel Journal of Mathematics》1998,108(1):109-138
Given anm-accretive operatorA in a Banach spaceX and an upper semicontinuous multivalued mapF: [0,a]×X→2
X
, we consider the initial value problemu′∈−Au+F(t,u) on [0,a],u(0)=x
0. We concentrate on the case when the semigroup generated by—A is only equicontinuous and obtain existence of integral solutions if, in particular,X* is uniformly convex andF satisfies β(F(t,B))≤k(t)β(B) for all boundedB⊂X wherek∈L
1([0,a]) and β denotes the Hausdorff-measure of noncompactness. Moreover, we show that the set of all solutions is a compactR
δ-set in this situation. In general, the extra condition onX* is essential as we show by an example in whichX is not uniformly smooth and the set of all solutions is not compact, but it can be omited ifA is single-valued and continuous or—A generates aC
o-semigroup of bounded linear operators. In the simpler case when—A generates a compact semigroup, we give a short proof of existence of solutions, again ifX* is uniformly (or strictly) convex. In this situation we also provide a counter-example in ℝ4 in which no integral solution exists.
The author gratefully acknowledges financial support by DAAD within the scope of the French-German project PROCOPE. 相似文献
14.
In the paper we introduce a transcendence degree of a zero-cycle on a smooth projective variety X and relate it to the structure of the motive of X. In particular, we show that in order to prove Bloch’s conjecture for a smooth projective complex surface X of general type with p
g
= 0 it suffices to prove that one single point of a transcendence degree 2 in X(ℂ), over the minimal subfield of definition k ⊂ ℂ of X, is rationally equivalent to another single point of a transcendence degree zero over k. This can be of particular interest in the context of Bloch’s conjecture for those surfaces which admit a concrete presentation,
such as Mumford’s fake surface, see [Mumford D., An algebraic surface with K ample, (K
2) = 9, p
g
= q = 0, Amer. J. Math., 1979, 101(1), 233–244]. 相似文献
15.
LetV(g, x, k, y) be the set of all pairs (X, F), whereX is an integral projective nodal curve withp
a(X)=g and card(Sing(X))=x andF is a rank 1 torsion free sheaf onX with deg(F)=k, card(Sing(F))=y andh
0(X, F)≥2. Here we study a general (X, F) εV(g, x, k, y) and in particular the Brill-Noether theory ofX and the scrollar invariants ofF. 相似文献
16.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
17.
Yasushi Taga 《Annals of the Institute of Statistical Mathematics》1971,23(1):355-363
Summary Let {X
n
},n=1,2,..., be a sequence of independent random variables distributed according to a distribution functionF(x) with finite variance,F
n
(x) be the empiric distribution function ofX
1,...,X
n
for eachn, andφ
(n)
*
andφ
* be optimum stratifications corresponding toF
n
(x) andF(x) respectively.
It is shown in this paper thatφ
(a)
*
tends almost surely toφ
* under a suitable criterion.
Institute of Statistical Mathematics 相似文献
18.
Let B
w
(ℓ
p
) denote the space of infinite matrices A for which A(x) ∈ ℓ
p
for all x = {x
k
}
k=1∞ ∈ ℓ
p
with |x
k
| ↘ 0. We characterize the upper triangular positive matrices from B
w
(ℓ
p
), 1 < p < ∞, by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are
stated and discussed. 相似文献
19.
ZhangYi LuTongyu 《高校应用数学学报(英文版)》2004,19(4):429-434
Let (X1,X2,…,Xn) and (Y1,Y2,…Yn) be real random vectors with the same marginal distributions,if (X1,X2,…,Xn)≤c(Y1,Y2,…Yn), it is showed in this paper that ∑i=1^n Xi≤cx∑i=1^n Yi and max1≤k≤n∑i=1^k Xi≤icx max1≤k≤n∑i=1^k Yi hold. Based on this fact,a more general comparison theorem is obtained. 相似文献
20.
M. Z. Garaev 《Monatshefte für Mathematik》2006,160(1):127-138
We obtain nontrivial estimates of character sums over short intervals for almost all moduli. These bounds and the method of
Karatsuba for solving multiplicative ternary problems are used to prove that for π(X)(1 + o(1)) primes p,p ≤ X, there are p(1 + o(1)) residue classes modulo p of the form xy (mod p), where 1 ≤ x, y ≤ p?(log p)1,087. We also prove that for any prime p there are p(1 + o(1)) residue classes modulo p of the form xy* (mod p), where 1 ≤ x, y ≤ p?(log p)1+o(1) and y* is defined by yy* ≡ 1 (mod p). 相似文献