共查询到20条相似文献,搜索用时 26 毫秒
1.
We study two questions posed by Johnson, Lindenstrauss, Preiss, and
Schechtman, concerning the structure of level sets of uniform and Lipschitz
quotient mappings from
. We show that if
, is a uniform quotient mapping then for every
has
a bounded number of components, each component of
separates
and the upper bound of the number of components depends
only on
and the moduli of co-uniform and uniform continuity of
.Next we prove that all level sets of any co-Lipschitz uniformly
continuous mapping from
to
are locally connected, and we show
that for every pair of a constant
and a function
with
, there exists a natural number
, so that
for every co-Lipschitz uniformly continuous map
with a
co-Lipschitz constant
and a modulus of uniform continuity
, there
exists a natural number
and a finite set
with
card
so that for all
has exactly
components,
has exactly
components and
each component of
is homeomorphic with the real line and
separates the plane into exactly 2 components. The number and form
of components of
for
are also described - they have a
finite tree structure. 相似文献
2.
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
3.
In this paper we show that, given a complete lattice
, the following three
lattices are the same: (1) the lattice of closure relations on
, (2) the lattice of meet-closed subsets of
, and (3) the lattice of complete join congruence relations on
. 相似文献
4.
Let Q(x, y) = 0 be an hyperbola in the plane. Given real numbers β ≡ β (2n)={ β ij } i,j ≥ 0,i+j ≤ 2n , with β00 > 0, the truncated Q-hyperbolic moment problem for β entails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x, y) = 0, such that
We prove that β admits a Q-representing measure μ (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated, has a column relation Q(X,Y) = 0, and the algebraic variety
associated to β satisfies card
In this case,
if
then β admits a rank
-atomic (minimal) Q-representing measure; if
then β admits a Q-representing measure μ satisfying
相似文献
5.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φx of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
6.
We compare the two recently introduced semidirect product operations
*r and
*rr within the lattice of e-varieties of locally inverse
semigroups. For each e-variety
which
contains all rectangular bands and is properly contained in the e-variety of all completely
simple semigroups, the inclusions
are proved where
is the e-variety of all semilattices and
the variety of all abelian
groups of exponent dividing q where q is any
integer greater than one. Some consequences for the class of finite locally inverse semigroups are also obtained. 相似文献
7.
8.
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
9.
We investigate the ideal structure of the Toeplitz algebra
of a totally ordered abelian group
. We show that the primitive ideals of
are parametrised by the disjoint union
of the duals
of the order ideals
of
, and identify the
hull-kernel topology on
when the chain of orderideals in
is isomorphic to a subset of
相似文献
10.
Maribel Loaiza 《Integral Equations and Operator Theory》2005,51(1):141-153
Let
and
be a finite collection of smooth curves in D. Given k points
consider the family
of all bounded and continuous functions on
with finite limits at
and radial limits at zk. We study the Toeplitz operator algebra
corresponding to Mr and we prove that its Calkin algebra is isomorphic to the algebra of all continuous functions on some compact set. This fact implies that the commutator of two Toeplitz operators with this kind of symbols is compact. We also prove that the semi-commutator of such Toeplitz operators is not compact, in general. 相似文献
11.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
12.
The probability that m randomly chosen elements
of a finite power associative loop
have prescribed orders and generate
is calculated in terms of certain constants
related to the action of Aut(
) on the subloop lattice of
. As an illustration, all meaningful
probabilities of random generation by elements of given orders are found for the smallest
nonassociative simple Moufang loop. 相似文献
13.
Hasse constants and their basic properties are introduced to facilitate the connection
between the lattice of subalgebras of an algebra
and the natural action of the automorphism group Aut(
) on
. These constants are then used to describe the lattice
of subloops of the smallest nonassociative simple Moufang loop. 相似文献
14.
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
15.
A class of bounded operators on Sobolev spaces 总被引:2,自引:0,他引:2
We describe a class of nonlinear operators which are bounded on the
Sobolev spaces
, for
and 1 < p <
. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on
, for
and 1 < p <
; this extends the result of J. Kinnunen [7], valid for s = 1.
Received: 5 December 2000 相似文献
16.
For an arbitrary (possibly infinite-dimensional) pre-symplectic test function
space
the family of Weyl algebras
, introduced in a previous work [1], is shown to constitute a continuous field of C*-algebras in the sense
of Dixmier. Various Poisson algebras, given as abstract (Fréchet-) *-algebras which
are C*-norm-dense in
, are constructed as domains for a Weyl quantization,
which maps the classical onto the quantum mechanical Weyl elements. This kind
of a quantization map is demonstrated to realize a continuous strict deformation
quantization in the sense of Rieffel and Landsman. The quantization is proved to
be equivariant under the automorphic actions of the full affine symplectic group.
The relationship to formal field quantization in theoretical physics is discussed by
suggesting a representation dependent direct field quantization in mathematically
concise terms.
Communicated by Joel FeldmanSubmitted 07/10/03, accepted 07/11/03 相似文献
17.
We consider the three-dimensional Schrödinger operators
and
where
, A is a magnetic potential generating a constant magnetic
field of strength
, and
where
decays fast enough at infinity. Then, A. Pushnitskis representation of the spectral shift function (SSF)
for the pair of operators
is well defined for energies
We study the behaviour of the associated representative of the equivalence class
determined by the SSF, in a neighbourhood of the Landau levels
Reducing our analysis to the study of the eigenvalue asymptotics for a family of
compact operators of Toeplitz type, we establish a relation between the type of the
singularities of the SSF at the Landau levels and the decay rate of V at infinity.
Communicated by Bernard HelfferSubmitted 23/09/03, accepted 15/01/04 相似文献
18.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
19.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
20.
Mark Pankov 《Journal of Geometry》2004,79(1-2):169-176
Let
be a finite-dimensional projective space
and
be the Grassmannian consisting of
all k-dimensional subspaces of
. In the paper we show that
transformations of
sending base subsets
to base subsets are induced by collineations of
to itself or to the dual projective space
.
This statement generalizes the main result of the authors paper [19]. 相似文献