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1.
The ℒ
p
spaces which were introduced by A. Pełczyński and the first named author are studied. It is proved, e.g., that (i)X is an ℒ
p
space if and only ifX* is and ℒ
q
space (p
−1+q
−1=1). (ii) A complemented subspace of an ℒ
p
space is either an ℒ
p
or an ℒ2 space. (iii) The ℒ
p
spaces have sufficiently many Boolean algebras of projections. These results are applied to show thatX is an ℒ∞ (resp. ℒ1) space if and only ifX admits extensions (resp. liftings) of compact operators havingX as a domain or range space. We also prove a theorem on the “local reflexivity” of an arbitrary Banach space.
This research was partially supported by NSF Grant# 8964. 相似文献
2.
It is shown that ifX is an ℒ⫗ space with separable dual, thenX has a quotient isomorphic toC(ω)α if, and only if, there is anɛ >0, such that theɛ-Szlenk index ofX is at leastα. It was previously known, that ifX is a separable ℒ⫗ space with a non-separable dual, thenX has a quotient isomorphic toC[0, 1].
Research partially supported by NSF Grant MCS-74-07509-A03. 相似文献
3.
For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the
associated crossed product C
*-algebras C(X)⋊
α,ℒℕ introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological
freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In
this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering
map is topologically free; the canonical embedding of C(X) into C(X)⋊
α,ℒℕ is a maximal abelian C
*-subalgebra of C(X)⋊
α,ℒℕ; any nontrivial two sided ideal of C(X)⋊
α,ℒℕ has non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊
α,ℒℕ is faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product
C
*-algebras of homeomorphism dynamical systems. 相似文献
4.
Hans-Joachim Baues 《Inventiones Mathematicae》1998,132(3):467-489
5.
Robin de Jong 《manuscripta mathematica》2009,129(3):273-292
Let X/S be a hyperelliptic curve of genus g over the spectrum of a discrete valuation ring. Two fundamental numerical invariants are attached to X/S: the valuation d of the hyperelliptic discriminant of X/S, and the valuation δ of the Mumford discriminant of X/S (equivalently, the Artin conductor). For a residue field of characteristic 0 as well as for X/S semistable the invariants d and δ are known to satisfy certain inequalities. We prove an exact formula relating d and δ with intersection theoretic data determined by the distribution of Weierstrass points over the special fiber, in the semistable
case. We also prove an exact formula for the stable Faltings height of an arbitrary curve over a number field, involving local
contributions associated to its Weierstrass points. 相似文献
6.
Kamil John 《Czechoslovak Mathematical Journal》2005,55(3):677-681
We observe that a separable Banach space X is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if ℒ(X, Y) is not reflexive for reflexive X and Y then ℒ(X
1, Y) is is not reflexive for some X
1 ⊂ X, X
1 having a basis.
This work was supported by the grants No. 201/03/0041 and No. 201/04/0090 of the Grant Agency of the Czech Republic and by
the grant No. A1019801 of the Academy of Sciences of the Czech Republic. 相似文献
7.
Tadeusz Figiel William B. Johnson Aleksander Pe?czyński 《Israel Journal of Mathematics》2011,183(1):199-231
The notion of the bounded approximation property = BAP (resp. the uniform approximation property = UAP) of a pair [Banach space, its subspace] is used to prove that if X is a ℒ
∞-space, Y a subspace with the BAP (resp. UAP), then the quotient X/Y has the BAP (resp. UAP). If Q: X → Z is a surjection, X is a ℒ
1-space and Z is a ℒ
p
-space (1 ≤ p ≤ ∞), then ker Q has the UAP. A complemented subspace of a weakly sequentially complete Banach lattice has the separable complementation property = SCP.
A criterion for a space with GL-l.u.st. to have the SCP is given. Spaces which are quotients of weakly sequentially complete
lattices and are uncomplemented in their second duals are studied. Examples are given of spaces with the SCP which have subspaces
that fail the SCP. The results are applied to spaces of measures on a compact Abelian group orthogonal to a fixed Sidon set
and to Sobolev spaces of functions of bounded variation on ℝ
n
. 相似文献
8.
Kilian Kilger 《The Ramanujan Journal》2008,17(3):321-330
Generally it is unknown, whether or not ∞ is a Weierstrass point on the modular curve X
0(N) if N is squarefree. A classical result of Atkin and Ogg states that ∞ is not a Weierstrass point on X
0(N), if N=pM with p prime, p
∤
M and the genus of X
0(M) zero. We use results of Kohnen and Weissauer to show that there is a connection between this question and the p-adic valuation of cusp forms under the Atkin–Lehner involution. This gives, in a sense, a generalization of Ogg’s Theorem
in some cases.
相似文献
9.
Let λ>1. We prove that every separable Banach space E can be embedded isometrically into a separable ℒ
∞
λ
-spaceX such thatX/E has the RNP and the Schur property. This generalizes a result in [2]. Various choices ofE allow us to answer several questions raised in the literature. In particular, takingE = ℓ2, we obtain a ℒ
∞
λ
-spaceX with the RNP such that the projective tensor product
containsc
0 and hence fails the RNP. TakingE=L
1, we obtain a ℒ
∞
λ
-space failing the RNP but nevertheless not containingc
0. 相似文献
10.
This is an investigation of the connections between bases and weaker structures in Banach spaces and their duals. It is proved,
e.g., thatX has a basis ifX* does, and that ifX has a basis, thenX* has a basis provided thatX* is separable and satisfies Grothendieck’s approximation property; analogous results are obtained concerning π-structures
and finite dimensional Schauder decompositions. The basic results are then applied to show that every separableℒ
p
space has a basis.
The second and third named authors have been supported by the NSF Grant GP 12997. 相似文献
11.
Li-Chien Shen 《The Ramanujan Journal》2009,18(1):61-72
We examine the significance of the values of the Weierstrass ℘ function at the points of order three in the period parallelogram. Based upon the well-known duplication formulae and the
differential equation of the Weierstrass ℘ function, we derive a set of identities involving the values of ℘ at these points.
相似文献
12.
Jie Gao Michael Langberg Leonard J. Schulman 《Discrete and Computational Geometry》2008,40(4):537-560
The analysis of incomplete data is a long-standing challenge in practical statistics. When, as is typical, data objects are
represented by points in ℝ
d
, incomplete data objects correspond to affine subspaces (lines or Δ-flats). With this motivation we study the problem of finding the minimum intersection radius
r(ℒ) of a set of lines or Δ-flats ℒ: the least r such that there is a ball of radius r intersecting every flat in ℒ. Known algorithms for finding the minimum enclosing ball for a point set (or clustering by several
balls) do not easily extend to higher-dimensional flats, primarily because “distances” between flats do not satisfy the triangle
inequality. In this paper we show how to restore geometry (i.e., a substitute for the triangle inequality) to the problem,
through a new analog of Helly’s theorem. This “intrinsic-dimension” Helly theorem states: for any family ℒ of Δ-dimensional convex sets in a Hilbert space, there exist Δ+2 sets ℒ′⊆ℒ such that r(ℒ)≤2r(ℒ′). Based upon this we present an algorithm that computes a (1+ε)-core set ℒ′⊆ℒ, |ℒ′|=O(Δ
4/ε), such that the ball centered at a point c with radius (1+ε)r(ℒ′) intersects every element of ℒ. The running time of the algorithm is O(n
Δ+1
dpoly (Δ/ε)). For the case of lines or line segments (Δ=1), the (expected) running time of the algorithm can be improved to O(ndpoly (1/ε)). We note that the size of the core set depends only on the dimension of the input objects and is independent of the input
size n and the dimension d of the ambient space.
An extended abstract appeared in ACM–SIAM Symposium on Discrete Algorithms, 2006.
Work was done when J. Gao was with Center for the Mathematics of Information, California Institute of Technology.
Work was done when M. Langberg was a postdoctoral scholar at the California Institute of Technology. Research supported in
part by NSF grant CCF-0346991.
Research of L.J. Schulman supported in part by an NSF ITR and the Okawa Foundation. 相似文献
13.
R. Grzlewicz 《Arkiv f?r Matematik》1991,29(1):73-81
Let ℒ(H) denote the space of operators on a Hilbert spaceH. We show that the extreme points of the unit ball of the space of continuous functionsC(K, ℒ(H)) (K-compact Hausdorff) are precisely the functions with extremal values. We show also that these extreme points are (a) strongly
exposed if and only if dimH<∞ and cardK<∞, (b) exposed if and only ifH is separable andK carries a strictly positive measure. 相似文献
14.
Let T ∈ ℒ(X) be a bounded operator on a complex Banach space X. If V is an open subset of the complex plane such that λ-T is of Kato-type for each λ ∈ V, then the induced mapping f(z) ↦ (z-T)f(z) has closed range in the Fréchet space of analytic X-valued functions on V. Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to
a sharper estimate of Nagy’s spectral residuum of T. Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and Putinar and the theory of coherent analytic
sheaves. 相似文献
15.
A. Rosenthal 《Israel Journal of Mathematics》1988,64(1):57-72
We generalize a result of R. Jewett [J]: IfT is an ergodic measure preserving transformation on (X, Ω,λ),T not necessarily invertible, there exists a strictly ergodicS acting on (Y, Θ,ν), whereY is compact, such that (X, Ω,λ, T) is measure theoretically isomorphic to (Y, Θ,ν, S). 相似文献
16.
17.
Two invertible dynamical systems (X, gA, μ, T) and (Y, ℬ, ν, S), where X, Y are metrizable spaces and T, S are homeomorphisms on X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X
0 of X of full measure to a subset Y
0 of Y of full measure such that ϕ|x
0 is continuous in the relative topology on X
0, ϕ
−1|Y
0 is continuous in the relative topology on Y
0 and ϕ(Orb
T
(x)) = Orb
Sϕ
(x) for μ-a.e. x ∈ X. In this article a finitary orbit equivalence mapping is shown to exist between any two irreducible Markov chains. 相似文献
18.
Beloslav Riečan 《Mathematica Slovaca》2010,60(5):655-664
The classical Poincaré strong recurrence theorem states that for any probability space (Ω, ℒ, P), any P-measure preserving transformation T, and any A ∈ ℒ, almost all points of A return to A infinitely many times. In the present paper the Poincaré theorem is proved when the σ-algebra ℒ is substituted by an MV-algebra of a special type. Another approach is used in [RIEČAN, B.: Poincaré recurrence theorem in MV-algebras. In: Proc. IFSA-EUSFLAT 2009 (To appear)], where the weak variant of the theorem is proved, of course, for arbitrary MV-algebras.
Such generalizations were already done in the literature, e.g. for quantum logic, see [DVUREČENSKIJ, A.: On some properties of transformations of a logic, Math. Slovaca 26 (1976), 131–137. 相似文献
19.
Jaime E. A. Rodriguez Oscar Paz la Torre Renato Vidal Martins Paulo Henrique Viana 《Bulletin of the Brazilian Mathematical Society》2008,39(1):137-155
We study curves of genus 3 over algebraically closed fields of characteristic 2 with the canonical theta characteristic totally
supported in one point. We compute the moduli dimension of such curves and focus on some of them which have two Weierstrass
points with Weierstrass directions towards the support of the theta characteristic. We answer questions related to order sequence
and Weierstrass weight of Weierstrass points and the existence of other Weierstrass points with similar properties.
– Dedicated to the treasured memory of our coauthor, Paulo Henrique Viana 相似文献
20.
V. M. Kopytov 《Algebra and Logic》2009,48(5):344-356
We create a method which allows an arbitrary group G with an infrainvariant system ℒ(G) of subgroups to be embedded in a group G* with an infrainvariant system ℒ(G*) of subgroups, so that G
α* ∩G ∈ ℒ(G) for every subgroup G
α* ∩G ∈ ℒ(G*) and each factor B/A of a jump of subgroups in ℒ(G*) is isomorphic to a factor of a jump in ℒ(G), or to any specified group H. Using this method, we state new results on right-ordered groups. In particular, it is proved that every Conrad right-ordered
group is embedded with preservation of order in a Conrad right-ordered group of Hahn type (i.e., a right-ordered group whose
factors of jumps of convex subgroups are order isomorphic to the additive group ℝ); every right-ordered Smirnov group is embedded
in a right-ordered Smirnov group of Hahn type; a new proof is given for the Holland–McCleary theorem on embedding every linearly
ordered group in a linearly ordered group of Hahn type. 相似文献