共查询到20条相似文献,搜索用时 31 毫秒
1.
M. Rudelson 《Israel Journal of Mathematics》1995,89(1-3):189-204
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω
S(ω)oT(ω)dω is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n
α
) for some absolute constantα<1.
We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big
dimension isomorphic to ak-cube.
Research supported in part by a grant of the Israel Academy of Sciences. 相似文献
2.
Let (Ω, Σ) be a measurable space, X a Banach space whose characteristic of noncompact convexity is less than 1, C a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C. We prove that a set-valued nonexpansive mapping T: C → KC(C) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T: Ω × C → KC(C) has a random fixed point. 相似文献
3.
Bálint Farkas 《Czechoslovak Mathematical Journal》2011,61(2):309-322
For a given bi-continuous semigroup (T(t))
t⩾0 on a Banach space X we define its adjoint on an appropriate closed subspace X° of the norm dual X′. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ(X°,X). We give the following application: For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(Ω) of bounded Baire measures
(endowed with the weak*-topology). We show that bi-continuous semigroups on M(Ω) are precisely those that are adjoints of
bi-continuous semigroups on Cb(Ω). We also prove that the class of bi-continuous semigroups on Cb(ω) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict
topology. In general, if is not a Polish space this is not the case. 相似文献
4.
S. A. Antonyan 《Mathematical Notes》1999,65(2):135-143
It is proved that a based-free action α of a given compact Lie groupG on the Hilbert cubeQ is equivalent to the standard based-free action σ if and only if the orbit spaceQ
0/α of the free partQ
0=Q* is aQ-manifold having the proper homotopy type of the orbit spaceQ
0/σ. The existence of an equivariant retraction (Q
0, σ)→(Q
0, α) is established. It is proved that for any TikhonovG-spaceX the family of all equivariant mapsX→ conG separates the points and the closed sets inX.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 163–174, February, 1999. 相似文献
5.
Siddhartha Bhattacharya 《Israel Journal of Mathematics》2003,137(1):211-221
Let Γ be a discrete group and fori=1,2; letα
i be an action of Γ on a compact abelian groupX
i by continuous automorphisms ofX
i. We study measurable equivariant mapsf: (X
1,α
1)→(X
2,α
2), and prove a rigidity result under certain assumption on the order of mixing of the underlying actions. 相似文献
6.
S. S. Podkorytov 《Journal of Mathematical Sciences》2011,175(5):609-619
Homotopy classes of mappings of a space X to the circle T form an Abelian group B(X) (the Bruschlinsky group). If a: X → T is a continuous mapping, then [a] denotes the homotopy class of a, and I
r
(a): (X × T)
r
→
\mathbbZ \mathbb{Z} is the indicator function of the rth Cartesian power of the graph of a. Let C be an Abelian group and let f: B(X) → C be a mapping. By definition, f has order not greater than r if the correspondence I
r
(a) → f([a]) extends to a (partly defined) homomorphism from the Abelian group of Z-valued functions on (X × T)
r
to C. It is proved that the order of f equals the algebraic degree of f. (A mapping between Abelian groups has degree at most r if all of its finite differences of order r +1 vanish.) Bibliography: 2 titles. 相似文献
7.
S. S. Podkorytov 《Journal of Mathematical Sciences》2009,161(3):454-459
Homotopy classes of mappings of a compact polyhedron X to the circle T form an Abelian group B(X), which is called the Bruschlinsky group and is cananically isomorphic to H
1 (X; ℤ), Let L be an Abelian group, and let f: B(X) → L be a function. One says that the order of f does not exceed r if for each mapping a: X → T the value f([a]) is ℤ-linearly expressed via the characteristic function I
r
(a): (X × T)
r
→ ℤ of (Γ
a
)
r
, where Γ
a
⊂ X × T is the graph of a. The (algebraic) degree of f is not greater than r if the finite differences of f of order r + 1 vanish. Conjecturally, the order of f is equal to the algebraic degree of f. The conjecture is proved in the case where dim X ≤ 2. Bibliography: 1 title. 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.
Wolfgang Adamski 《Israel Journal of Mathematics》1989,65(1):79-95
Let (X,A) be a measureable space andT:X →X a measurable mapping. Consider a family ℳ of probability measures onA which satisfies certain closure conditions. IfA
0⊂A is a convergence class for ℳ such that, for everyA ∈A
0, the sequence ((1/n) Σ
i
=0/n−1
1
A
∘T
i) converges in distribution (with respect to some probability measurev ∈ ℳ), then there exists aT-invariant element in ℳ. In particular, for the special case of a topological spaceX and a continuous mappingT, sufficient conditions for the existence ofT-invariant Borel probability measures with additional regularity properties are obtained. 相似文献
10.
Dumitru Popa 《Proceedings Mathematical Sciences》2009,119(2):221-230
Let Ω be a compact Hausdorff space, X a Banach space, C(Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω, X) → Y a bounded linear operator and U
#, U
# two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π
s
(C(Ω, X), Y); (β)U
# ∈ Π
s
(C(Ω), Π
s
(X, Y)); (γ) U
# ε Π
s
(X, Π
s
(C(Ω), Y)). A general result, [10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C([0, 1], l
p
) with values in l
1 satisfies (α), (β) and (γ), which show that the above implication is the best possible result. 相似文献
11.
Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type 总被引:17,自引:0,他引:17
W. A. Kirk 《Israel Journal of Mathematics》1974,17(4):339-346
LetX be a Banach space,K a nonempty, bounded, closed and convex subset ofX, and supposeT:K→K satisfies: for eachx∈K, lim sup
i→∞{sup
y∈K
‖t
ix−Tiy∼−‖x−y‖}≦0. IfT
N is continuous for some positive integerN, and if either (a)X is uniformly convex, or (b)K is compact, thenT has a fixed point inK. The former generalizes a theorem of Goebel and Kirk for asymptotically nonexpansive mappings. These are mappingsT:K→K satisfying, fori sufficiently large, ‖Tix−Tiy‖≦k
i‖x−y∼,x,y∈K, wherek
i→1 asi→∞. The precise assumption in (a) is somewhat weaker than uniform convexity, requiring only that Goebel’s characteristic of
convexity, ɛ0 (X), be less than one.
Research supported by National Science Foundation Grant GP 18045. 相似文献
12.
Xiaotao Sun 《Inventiones Mathematicae》2008,173(2):427-447
Let X be a smooth projective variety of dimension n over an algebraically closed field k with char(k)=p>0 and F:X→X
1 be the relative Frobenius morphism. For any vector bundle W on X, we prove that instability of F
*
W is bounded by instability of W⊗Tℓ(Ω1
X
) (0≤ℓ≤n(p-1)) (Corollary 4.9). When X is a smooth projective curve of genus g≥2, it implies F
*
W being stable whenever W is stable.
Dedicated to Professor Zhexian Wan on the occasion of his 80th birthday. 相似文献
13.
Andrea Sambusetti 《manuscripta mathematica》1999,99(4):541-560
We prove that MinEnt (Y) ∥Y∥ = MinEnt(X) ∥X∥, for manifolds Y whose fundamental group is a subexponential extension of the fundamental group of some negatively curved, locally symmetric
manifold X. This is a particular case of a more general result holding for an arbitrary representation ρ : π1 (Y) →π1 (X), which relates the minimal entropy and the simplicial volume of X to some invariants of the couple (Y, ker (ρ)). Then, we discuss some applications to the minimal volume problem and to Einstein metrics.
Received: 23 December 1998 相似文献
14.
Aut(Ω) denotes the group of all order preserving permutations of the totally ordered set Ω, and if e ≤ u ∈ Aut(Ω), then B
u
Aut(Ω) denotes the subgroup of all those permutations bounded pointwise by a power of u. It is known that if Aut(Ω) is highly transitive, then Aut(Ω) has just five normal subgroups. We show that if Aut(Ω) is highly
transitive and u has just one interval of support, then B
u
Aut(Ω) has normal subgroups, and there is a certain ideal of the lattice of subsets of (), the power set of the integers, such that the lattice of normal subgroups of every such Aut(Ω) is isomorphic to .
To Bernhard Banaschewski on the occasion of his 80th birthday. 相似文献
15.
Let Ω be a bounded domain of the complex plane whose boundary is a closed Jordan curve and (F
n
)
n≥0 the sequence of Faber polynomials of Ω. We say that a bounded linear operator T on a separable Banach space X is Ω-hypercyclic if there exists a vector x of X such that {F
n
(T)x: n ≥ 0} is dense in X. We show that many of the results in the spectral theory of hypercyclic operators involving the unit disk or its boundary
have Ω-hypercyclic counterparts which involve the domain Ω or its boundary. The influence of the geometry of Ω or the smoothness
of its boundary on Faber-hypercyclicity is also discussed. 相似文献
16.
Hans-Joachim Baues 《Inventiones Mathematicae》1998,132(3):467-489
17.
Marco Antei 《Israel Journal of Mathematics》2011,186(1):427-446
Let S be a connected Dedekind scheme and X an S-scheme provided with a section x. We prove that the morphism between fundamental group schemes π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) induced by the canonical morphism from X to its Albanese scheme Alb
X/S
(when the latter exists) fits in an exact sequence of group schemes 0 → (NS
X/S
τ
)⋎ → π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) → 0, where the kernel is a finite and flat S-group scheme. Furthermore, we prove that any finite and commutative quotient pointed torsor over the generic fiber X
η
of X can be extended to a finite and commutative pointed torsor over X. 相似文献
18.
It is shown that ifT is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε ℤ is orthonormal and spans L0
2(Ω,B,m), then for any integerk ≠ 0, the random variablesX o Tnk,n ε ℤ generateB modulom. 相似文献
19.
M. C. Crabb 《Journal of Fixed Point Theory and Applications》2007,2(2):171-193
We describe an equivariant version (for actions of a finite group G) of Dold’s index theory, [10], for iterated maps. Equivariant Dold indices are defined, in general, for a G-map U → X defined on an open G-subset of a G-ANR X (and satisfying a suitable compactness condition). A local index for isolated fixed-points is introduced, and the theorem
of Shub and Sullivan on the vanishing of all but finitely many Dold indices for a continuously differentiable map is extended
to the equivariant case. Homotopy Dold indices, arising from the equivariant Reidemeister trace, are also considered.
相似文献
20.
I. Kocsis 《Acta Mathematica Hungarica》2008,118(4):307-312
Let X ⊂ ℝ be an interval of positive length and define the set Δ = {(x, y) ∈ X × X | x ≧ y}. We give the solution of the equation
which holds for all (x, y) ∈ Δ and (u, υ) ∈ Δ, where the functions F: X → X, G
1: Δ → X, G
2: Δ → X, and G: F(X, X) × F(X, X) → X are continuous and strictly monotonic in each variable.
This research was supported by the Hungarian Scientific Research Fund (OTKA), grant No. T-043080. 相似文献