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1.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
2.
In this note we prove that the Laplacian with generalized Wentzell boundary
conditions on an open bounded regular domain in
defined by
generates an analytic semigroup of angle
on
for every > 0 and
(for the definition of
cf. (1.3)).Received: 13 July 2002 相似文献
3.
Let
be a locally compact group. Consider the Banach algebra
, equipped with the first Arens multiplication, as well as the
algebra LUC
, the dual of the space of bounded left uniformly
continuous functions on
, whose product extends the convolution in
the measure algebra M
. We present (for the most interesting case
of a non-compact group) completely different - in particular,
direct - proofs and even obtain
sharpened versions of
the results, first proved by Lau-Losert in [9] and Lau in
[8], that the topological centres of the latter algebras
precisely are
and M
, respectively. The special interest of
our new approach lies in the fact that it shows a fairly general pattern
of solving the topological centre problem for various kinds of Banach
algebras; in particular, it avoids the use of any measure theoretical
techniques. At the same time, deriving both results in perfect
parallelity, our method reveals the nature of their close relation.Received: 1 January 2002 相似文献
4.
Let M be a right R-module,
the class of all M-small modules, and P a projective cover of M in
[M]. We consider the torsion theories
= (
),
= (
), and
= (
) in
[M], where
is the torsion theory generated by
is the torsion theory cogenerated by
, and
is the dual Lambek torsion theory. We study some conditions for
to be cohereditary, stable, or split, and prove that Rej(M,
) = M
=
(=
=
)
=
GenM(P)
.2000 Mathematics Subject Classification: 16S90 相似文献
5.
6.
Let p be a prime,
a finite p-group,
any finite group with order divisible by p,
and
any action of
on
. We show that the cardinality of the set of all derivations
with respect to this action is a multiple of
p. This
generalises theorems of Frobenius and Hall.
Received: 16 June 2003 相似文献
8.
We prove that a finite group G is
-constrained if and only if it contains a nilpotent subgroup
I satisfying
for all
.Received: 22 July 2002 相似文献
9.
10.
To every egglike inversive plane
there is associated a family
of involutions of the point set of
such that
circles of
are the fixed point sets of the involutions in
. Korchmaros and Olanda characterized a family
of involutions on a set of size n2 + 1to be
for
an egglike inversive plane of order n by four conditions. In this
paper, we give an alternative proof where the Galois space PG(3,n) in
which
is embedded is built up directly by using concepts and
results on finite linear spaces. 相似文献
11.
Let C be a set of objects in a triangulated compactly generated category
We denote by
the smallest suspended subcategory closed under coproducts which contains C (the smallest cosuspended subcategory closed under products which contains
C). We prove that if C is a set of compacts objects then
is a t-structure in
where TC
I is the dual of C with respect to an injective cogenerator
I in the category Mod
C. Moreover, we show that:
C is a tilting set if and only if
And, this is equivalent to TCI is a cotilting object in
Received: 28 March 2003 相似文献
12.
13.
The number of Fq
-rational points of a plane non-singular algebraic curve
defined over a finite field Fq
is computed, provided that the generic point of
is not an inflexion and that
is Frobenius non-classical with respect to conics.
Received: 18 March 2003 相似文献
14.
Let X = {1, . . . ,
n}, and let
be a family of subsets
of X. Given the size of
, at least how many pairs
of elements of
must be disjoint? In
this paper we give a lower bound for the number of disjoint
pairs in
. The bound we obtain is
essentially best possible. In particular, we give a new proof of
a result of Frankl and of Ahlswede, that if
satisfies
then
contains at least as
many disjoint pairs as X(r).The situation is rather different if we restrict our
attention to
: then we are asking for
the minimum number of edges spanned by a subset of the Kneser
graph of given size. We make a conjecture on this lower bound,
and disprove a related conjecture of Poljak and Tuza on the
largest bipartite subgraph of the Kneser graph.* Research partially supported by NSF grant
DMS-9971788 相似文献
15.
Given a continuous linear operator T L(x) defined on a separable
-space X, we will show that T satisfies the Hypercyclicity Criterion if and only if for any strictly increasing sequence of positive integers
such that
the sequence
is hypercyclic. In contrast we will also prove that, for any hypercyclic vector x X of T, there exists a strictly increasing sequence
such that
and
is somewhere dense, but not dense in X. That is, T and
do not share the same hypercyclic vectors. 相似文献
16.
Marilyn Breen 《Aequationes Mathematicae》2004,67(3):263-275
Summary.
We establish the following Helly-type result for infinite families
of starshaped sets in
Define the function f on
{1, 2} by
f(1) = 4,
f(2) = 3.
Let
be a fixed positive number, and let
be a uniformly bounded family of compact sets
in the plane. For k = 1, 2, if every
f(k)
(not necessarily distinct) members of
intersect in a starshaped set whose
kernel contains a k-dimensional
neighborhood of radius
, then
is a starshaped set whose kernel is at least
k-dimensional.
The number f(k) is best in each case.
In addition, we present a few results concerning the dimension of
the kernel in an intersection of starshaped sets in
Some of these involve finite families of sets, while others
involve infinite families and make use of the Hausdorff metric. 相似文献
17.
Let
be an artin algebra which has only finitely many isomorphism classes of
non-faithful indecomposable modules. We show that large indecomposable
-modules contain large free submodules.
Received: 12 April 2003 相似文献
18.
Let
be the Hecke algebra of the symmetric group
over a field K of characteristic
and
a primitive
-th root of one in K. We show that an
-module is projective if and only if its restrictions to any
-parabolic subalgebra of
is projective.
Moreover, we give a new construction of blocks of
-parabolic subalgebras, in terms of skew group algebras over local commutative
algebras.
Received: 30 June 2003 相似文献
19.
In this work we determine the group of modular automorphisms of the
Drinfeld modular curve
for any nonconstant polynomial
.Received: 19 September 2002 相似文献
20.
For a class of stable planes we define a notion of isotopy equivalence with
respect to that class and prove that any two planes of a certain class of
-planes comprising all affine
-planes are isotopy equivalent. Furthermore we obtain that all affine
-planes are isotopy equivalent in the class of affine
-planes. Finally we give an example which shows that this approach cannot be easily generalized
to 2-dimensional projective planes, and we outline a different way for a
possible generalization.Received: 27 April 2001 相似文献