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1.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
2.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
3.
Humio Ichimura 《Archiv der Mathematik》2006,87(6):539-545
Let p be an odd prime number and
. Let
be the classical Stickelberger ideal of the group ring
. Iwasawa [6] proved that the index
equals the relative class number
of
. In [2], [4] we defined for each subgroup H of G a Stickelberger ideal
of
, and studied some of its properties. In this note, we prove that when
mod 4 and [G : H] = 2, the index
equals the quotient
.
Received: 13 January 2006 相似文献
4.
For an l-graph
, the Turán number
is the maximum number of edges in an n-vertex l-graph
containing no copy of
. The limit
is known to exist [8]. The Ramsey–Turán density
is defined similarly to
except that we restrict to only those
with independence number o(n). A result of Erdős and Sós [3] states that
as long as for every edge E of
there is another edge E′of
for which |E∩E′|≥2. Therefore a natural question is whether there exists
for which
.
Another variant
proposed in [3] requires the stronger condition that every set of vertices of
of size at least εn (0<ε<1) has density bounded below by some threshold. By definition,
for every
. However, even
is not known for very many l-graphs
when l>2.
We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we
construct, for each l≥3, infinitely many l-graphs
for which
.
We also prove that the 3-graph
with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies
. The existence of a hypergraph
satisfying
was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based
on different ideas and is simpler than these earlier proofs.
* Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P.
Sloan Research Fellowship.
† Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529. 相似文献
5.
The purpose of this paper is to give new and general characterizations for uniform dichotomy and uniform exponential dichotomy
of evolution families on the real line. We consider two general classes denoted
and
and we prove that if V,W are Banach function spaces with
and
, then the admissibility of the pair
for an evolution family
implies the uniform dichotomy of
. In addition, we consider a subclass
and we prove that if
, then the admissibility of the pair
implies the uniform exponential dichotomy of the family
. This condition becomes necessary if
. Finally, we present some applications of the main results. 相似文献
6.
J. J. Grobler 《Integral Equations and Operator Theory》2007,57(1):83-99
For a probability space
we denote the marginal measures of
, defined on Σ and Λ respectively, by
and
. If ρ is a function norm defined on
marginal function norms ρ1 and ρ2 are defined on
and
. We find conditions which guarantee Lρ 1 + Lρ 2 to be embedded in Lρ as a closed subspace. The problem is encountered in Statistics when estimating a bivariate distribution with known marginals.
We find a condition which, applied to the binormal distribution in L2, improves some known conditions. 相似文献
7.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
8.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
9.
Abstract
By
we denote the set of all propositional formulas. Let
be the set of all clauses. Define
. In Sec. 2 of this paper we prove that for normal modal logics
, the notions of
-expansions and
-expansions coincide. In Sec. 3, we prove that if I consists of default clauses then the notions of
-expansions for I and
-expansions for I coincide. To this end, we first show, in Sec. 3, that the notion of
-expansions for I is the same as that of
-expansions for I.
The project is supported by NSFC 相似文献
10.
11.
If
is an initially hereditary family of finite subsets of positive integers (i.e., if
and G is initial segment of F then
) and M an infinite subset of positive integers then we define an ordinal index
. We prove that if
is a family of finite subsets of positive integers such that for every
the characteristic function χF is isolated point of the subspace
of { 0,1 }N with the product topology then
for every
infinite, where
is the set of all initial segments of the members of
and ω1 is the first uncountable ordinal. As a consequence of this result we prove that
is Ramsey, i.e., if
is a partition of
then there exists an infinite subset M of positive integers such that
where [M]< ω is the family of all finite subsets of M. 相似文献
12.
13.
Mowaffaq Hajja 《Results in Mathematics》2006,49(3-4):237-263
An edge-incentric d-simplex is defined to be a d-simplex S which admits a (d − 1)-sphere that touches all the edges of S internally. The center of such a sphere is called the edge-incenter of S and is denoted by
. Equivalently, S is edge-incentric if and only if its vertices are the centers of d + 1 (d − 1)-spheres in mutual external touch, and for this reason one may call such an S a balloon d-simplex. An orthocentric d-simplex is a d-simplex in which the altitudes are concurrent. The point of concurrence is called the orthocenter and is denoted by
. The spaces of edge-incentric and of orthocentric d-simplices have the same dimension d in the sense that a d-simplex in either space can be parametrized, up to shape, by d numbers. Edge-incentric and orthocentric tetrahedra are the first two of the four special classes of tetrahedra studied in
[1, Chapter IX.B, pp. 294–333].
The degree of regularity implied by the coincidence of two or more centers of a general d-simplex is investigated in [8], where it is shown that the coincidence of the centroid
, the circumcenter
, and the incenter
does not imply much regularity. For an orthocentric d-simplex S, however, it is proved in [9] that if any two of the centers
, and
coincide, then S is regular. In this paper, the same question is addressed for edge-incentric d-simplices. Among other things, it is proved that if any three of the centers
, and
of an edge-incentric d-simplex S coincide, then S is regular, and it is also shown that none of the coincidences
, and
implies regularity (except when d ≤ 3, d ≤ 4, and d ≤ 6, respectively). In contrast with the afore-mentioned results for orthocentric d-simplices, this emphasizes once more the feeling that, regarding many important properties, orthocentric d-simplices are the true generalizations of triangles.
Several open questions are posed.
Received: June 19, 2006. 相似文献
14.
Let G be a connected simply connected almost
-simple algebraic group with
non-compact and
a cocompact congruence subgroup. For any homogeneous manifold
of finite volume, and a
, we show that the Hecke orbit T
a
(x
0
H) is equidistributed on
as
, provided H is a non-compact commutative reductive subgroup of G. As a corollary, we generalize the equidistribution result of Hecke points ([COU], [EO1]) to homogeneous spaces G/H. As a concrete application, we describe the equidistribution result in the rational matrices with a given characteristic
polynomial.
The second author partially supported by DMS 0333397.
Received: May 2005 Revision: March 2006 Accepted: June 2006 相似文献
15.
For a contraction operator T with spectral radius less than one on a Banach space
, it is shown that the factorization of certain L1 functions by vectors x in
and x*. in
, in the sense that
for n ≧ 0, implies the existence of invariant subspaces for T. Explicit formulae for such factorizations are given in the case of weighted composition operators on reproducing kernel
Hilbert spaces. An interpolation result of McPhail is applied to show how this can be used to construct invariant subspaces
of hyperbolic weighted composition operators on H2.
Received: 1 November 2005 相似文献
16.
Alina Iacob 《Archiv der Mathematik》2005,85(4):335-344
We consider two pairs of complete hereditary cotorsion theories
on the category of left R-modules, such that
We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules
can be computed either using a left
of M and a left
of M or using a right
a right
of N.
Received: 17 December 2004 相似文献
17.
Stefan Gille 《Archiv der Mathematik》2007,88(4):333-343
Let
be a closed subscheme of the noetherian scheme X. We show that if X has a dualizing complex
then there exists a dualizing complex
of Z such that there is an isomorphism of coherent Witt groups
for all
.
Received: 3 March 2006 相似文献
18.
Let Φ be an irreducible crystallographic root system with Weyl group W and coroot lattice
, spanning a Euclidean space V. Let m be a positive integer and
be the arrangement of hyperplanes in V of the form
for
and
. It is known that the number
of bounded dominant regions of
is equal to the number of facets of the positive part
of the generalized cluster complex associated to the pair
by S. Fomin and N. Reading.
We define a statistic on the set of bounded dominant regions of
and conjecture that the corresponding refinement of
coincides with the $h$-vector of
. We compute these refined numbers for the classical root systems as well as for all root systems when m = 1 and verify the conjecture when Φ has type A, B or C and when m = 1. We give several combinatorial interpretations to these numbers in terms of chains of order ideals in the root poset of Φ,
orbits of the action of W on the quotient
and coroot lattice points inside a certain simplex, analogous to the ones given by the first author in the case of the set
of all dominant regions of
. We also provide a dual interpretation in terms of order filters in the root poset of Φ in the special case m = 1.
2000 Mathematics Subject Classification Primary—20F55; Secondary—05E99, 20H15 相似文献
19.
We prove that for any continuous piecewise monotone or smooth interval map f and any subset
of the set of periods of periodic trajectories of f, there is another map
such that the set of periods of periodic trajectories common for f and
, which is denoted by
, coincides with
. At the same time, for each integer
, there exists a continuous map f such that
for any map
if
is an infinite set.
Dedicated to Vladimir Igorevich Arnold 相似文献
20.
The aim of the present paper is to introduce a metric locally convex topology on the space
of δ-psh functions in the Cegrell class
. We prove that with this topology
is a non-separable and non-reflexive Fréchet space. At the same time, we extend the Monge–Ampère operator from the class
to
. 相似文献