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1.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献
2.
For two complex Banach spaces X and Y,
(B
X; Y) will denote the space of bounded and continuous functions from B
X
to Y that are holomorphic on the open unit ball. The numerical radius of an element h in
(B
X; X) is the supremum of the set
. We prove that every complex Banach space X with the Radon-Nikodym property satisfies that the subset of numerical radius attaining functions in
(B
X; X) is dense in
(B
X; X). We also show the denseness of the numerical radius attaining elements of
in the whole space, where
is the subset of functions in
which are uniformly continuous on the unit ball. For C(K) we prove a denseness result for the subset of the functions in
(B
C(K); C(K)) which are weakly uniformly continuous on the closed unit ball. For a certain sequence space X, there is a 2-homogenous polynomial P from X to X such that for every R > e, P cannot be approximated by bounded and numerical radius attaining holomorphic functions defined on RB
X
. If Y satisfies some isometric conditions and X is such that the subset of norm attaining functions of
(B
X; ℂ) is dense in
(B
X; ℂ), then the subset of norm attaining functions in
(B
X; Y) is dense in the whole space.
The first author was supported in part by D.G.E.S. Project BFM2003-01681.
The second author’s work was performed during a visit to the Departamento de Análisis Matem’atico of Universidad de Granada,
with a grant supported by the Korea Research Foundation under grant (KRF-2002-070-C00006). 相似文献
3.
N. I. Osetinskii 《Computational Mathematics and Modeling》2008,19(1):45-56
We consider the classification of generalized linear controllable systems over the field
= ℂ or
= ℝ under transformations defined by the action of the group GL
n
(
) × GL
n
(
). We review the recent results of Cobb, Helmke, Shayman, Zhou, Hinrichsen, O’Halloran, and others on the geometric structure
of the set of orbits C
n,m
(
) of generalized linear controllable systems, which in particular prove smoothness, compactness, and projectivity of C
n,m
(
) and evaluate its dimension. We show that C
n,m
(
) is a natural compactification of the set of orbits of ordinary linear controllable systems ∑
n,m
(
) and the boundary C
n,m
(
) − ∑
n,m
(
) consists of the orbits of singular generalized systems.
__________
Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 153–166, 2004. 相似文献
4.
V. M. Petrogradsky 《Israel Journal of Mathematics》1999,113(1):323-339
Suppose that
% MathType!End!2!1! is a variety of Lie algebras, and letc
n(
% MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF(
% MathType!End!2!1!,X) of the variety
% MathType!End!2!1!. We consider an exponential generating function
% MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided
the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms
of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety.
Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands.
The main observation here is thatC(
% MathType!End!2!1!),z) behaves like a composition of three functionsC(
% MathType!End!2!1!),z), exp(z), andC(
% MathType!End!2!1!),z).
Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where
he was DAAD-fellow. 相似文献
5.
Let
be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G,
contains one and only one Sylow p-subgroup of G. A subgroup H of G is said to be
-permutable in G if H permutes with every member of
. In this paper we characterize p-nilpotency of finite groups G; we will assume that some minimal subgroups or 2-minimal subgroups of G are
-permutable in G. Moreover, the duals of some recent results are obtained.
Supported by the NSF of China(10571128) and the NSF of Colleges and Suzhou City Senior Talent Supporting Project.
Project supported in part by NSF of China (10571181), NSF of Guangdong Province (06023728) and ARF(GDEI).
Project supported in part by the NSF for youth of Shanxi Province (2007021004) and TianYuan Fund of Mathematics of China (10726002). 相似文献
6.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
7.
We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H
1, which may be considered over
and
. We also draw corollaries for the corresponding Hardy spaces over
2 and
2.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
8.
Judita Lihová 《Czechoslovak Mathematical Journal》1999,49(1):67-80
Let
be a partially ordered set, Int
the system of all (nonempty) intervals of
partially ordered by the set-theoretical inclusion
. We are interested in partially ordered sets
with Int
isomorphic to Int
. We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If
is a directed partially ordered set, the only
with Int
isomorphic to Int
are
corresponding to direct decompositions
of
(
denotes the dual of
. The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11]. 相似文献
9.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
10.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
11.
ALAIN HÉNAUT 《Geometriae Dedicata》1997,65(1):89-101
A d-web in (
,0) is given by d complex analytic foliations of codimension one in (
,0) which are in general position. A d-web
in (
,0) is linear if all the leaves are (pieces of) hyperplanes in
and
is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in
of degree d. We characterize linear webs in (
,0). We give explicit conditions under which a linear d-web in (
,0) is algebraic and we obtain equations for
in this case. Some related problems are discussed and some questions are posed. 相似文献
12.
Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius
-homomorphism. For
, this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space,
the
th symmetric power of X, and
the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map
defined by the formula
identifies the space
with the space of all Frobenius
-homomorphisms of the algebra
into
with the weak topology. 相似文献
13.
We prove that for almost allσ ∈G ℚ the field
has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→
there exists a point a ∈
such thatϕ(a) ∈ ℤr. We then say that
is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields
other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ. 相似文献
14.
S. Norvidas 《Lithuanian Mathematical Journal》2006,46(4):446-458
Let, for σ > 0,
be the set of complex functions f ∈ L
1 (ℝ) with the Fourier transforms
vanishing outside the interval [−σ; σ]. In this paper, we study the problem of the best approximation of the Dirac function δ (which has the Fourier transform with widest support supp
) by functions
. More precisely, we consider the quantity inf
and its extremal functions
.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 548–564, October–December, 2006. 相似文献
15.
Hoai-Minh Nguyen 《Journal d'Analyse Mathématique》2007,101(1):367-395
In this paper, we prove the estimate
, for every δ ∈ (0, ℓN), where C = C(N) is a positive constant depending only on N and
. We show that the constant ℓN in this estimate is optimal. We also present a class of maps from
into
, strictly larger than
, on which we can define the notion of degree and for which the previous inequality still holds. 相似文献
16.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献
17.
N. V. Smorodina 《Journal of Mathematical Sciences》2007,145(2):4914-4922
Let ξ(t), t ∈ [0, 1], be a strictly stable process with an index of stability α ∈ (0, 2). By
we denote the law of ξ in the Skorokhod space
[0,1]. For arbitrary strictly stable process ξ, we construct a semigroup of transformations of
[0, 1] for which the measure
is quasi-invariant. For strictly stable processes with positive and negative jumps, we construct a group of transformations
of
[0, 1] for which the measure
is quasi-invariant. In the symmetric case, this group is a group of invariant transformations. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 135–149. 相似文献
18.
We consider a Skorohod map
which takes paths in
to paths which stay in the positive orthant
. We let
be the domain of definition of
. A convex and lower semi-continuous function
and a set
are given. We are concerned with the calculation of the infimum of the value
for t ⩾ 0 and absolutely continuous
subject to the conditions
and
. We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state
distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems.
This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for
its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations
of heavily loaded queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
19.
For a given centred convex bodyK of ℝ,n≥3, let
be the class of all convex bodies with the same projection body asK. The question whetherK can be expressed as a Blaschke average of two non-homothetic bodies from
is considered. Necessary and sufficient conditions onK to be Blaschke decomposable in
are given.
The paper provides also a characterization of the bodiesK such that the Blaschke indecomposable bodies in
are dense in
itself. 相似文献
20.
N. V. Smorodina 《Journal of Mathematical Sciences》2007,147(4):6950-6957
Let ξ(t), t ∈ [0, 1], be a jump Lévy process. We denote by
the law of ξ in the Skorokhod space
[0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of
-preserving transformations of the space
[0, 1]. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 175–188. 相似文献