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1.
The paper investigates L
p
convergence and Marcinkiewicz-Zygmund strong laws of large numbers for random elements in a Banach space under the condition
that the Banach space is of Rademacher type p, 1 < p < 2. The paper also discusses L
r
convergence and L
r
bound for random elements without any geometric restriction condition on the Banach space. 相似文献
2.
Michael Joachim 《Mathematische Annalen》2003,327(4):641-670
We define K-homology groups K
*
() for small C
*
-categories in terms of Hilbert modules over the C
*
-category . We also define a functor A
f
from the category of small C
*
-categories into the category of C
*
-algebras and show that there is a natural isomorphism
. In addition, we give an easy construction of a functor
from the category of C
*
-algebras into the category of symmetric spectra which represents K-homology, i.e. we show that the functor
comes with a natural isomorphism
for C
*
-algebras A. It then follows that the composition
A
f
provides a functor that can be used in the Davis-Lück approach for constructing the Baum-Connes map. 相似文献
3.
4.
We classify graph C
*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to
strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C
*-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence
of such algebras, without using the boundary operator algebra. A direct relation is given between the K
1-group of the algebra and the cycle space of the graph.
We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K
0(
Ч) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University
College. 相似文献
5.
L
p
approximation capability of radial basis function (RBF) neural networks is investigated. If g: R
+1 → R
1 and ∈ L
loc
p
(R
n
) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L
p
(K) with any accuracy for any compact set K in R
n
, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
6.
Humio Ichimura 《Archiv der Mathematik》2011,96(6):555-563
Let p be an odd prime number, and pn0{p^{n_0}} the highest power of p dividing 2
p−1 − 1. Let Kn=Q(zpn+1){K_n={\bf Q}(\zeta_{p^{n+1}})} and Ln,j=Kn+(z2j+2){L_{n,j}=K_n^+(\zeta_{2^{j+2}})} for j ≥ 0. Let hn*{h_n^*} be the relative class number of K
n
, and h
n,j
the class number of L
n,j
, respectively. Let n be an integer with n ≥ n
0. We prove that if the ratio hn*/hn-1*{h_n^*/h_{n-1}^*} is odd, then h
n,j
/h
n−1,j
is odd for any j ≥ 0. 相似文献
7.
Elena V. Vernigora 《Journal of Mathematical Sciences》2012,182(1):108-116
We consider the construction of of an inversive congruential generator over a Galois ring of odd dimension p
l
, whichwas proposed by Solé and Zinoviev for p = 2. Using the estimates of trigonometric sums on the sequences of pseudorandom numbers, we obtain the estimates of a discrepant
function, a generated sequence of pseudorandom numbers, and the associated sequence of two-dimensional “overlapping” points. 相似文献
8.
For a fixed prime p, let C
p
denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f
2 (x) + B (x) g
2 (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa’s method. 相似文献
9.
Let X be a Banach space, K be a scattered compact and T: B
C(K) → X be a Fréchet smooth operator whose derivative is uniformly continuous. We introduce the smooth biconjugate T**: B
C(K)** → X** and prove that if T is noncompact, then the derivative of T** at some point is a noncompact linear operator. Using this we conclude, among other things, that either
is compact or that ℓ1 is a complemented subspace of X*. We also give some relevant examples of smooth functions and operators, in particular, a C
1,u
-smooth noncompact operator from B
c
O which does not fix any (affine) basic sequence.
P. Hájek was supported by grants A100190502, Institutional Research Plan AV0Z10190503. 相似文献
10.
An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric characterizations, up to isometry, of the unit ball of the dual space of a JB*-triple, and up to complete isometry, of one-sided ideals in C*-algebras.Mathematics Subject Classification (2000):17C65, 46L07Both authors are supported by NSF grant DMS-0101153 相似文献
11.
In this paper, we characterize a C
*-subalgebra C
*(x) of B(H), generated by a single operator x. We show that if x is polar-decomposed by aq, where a is the partial isometry part and q is the positive operator part of x, then C
*(x) is *-isomorphic to the groupoid crossed product algebra
Aq×a\mathbbGa\mathcal{A}_{q}\times_{\alpha }\mathbb{G}_{a}
, where
Aq=C*(q)\mathcal{A}_{q}=C^{*}(q)
and
\mathbbGa\mathbb{G}_{a}
is the graph groupoid induced by a partial isometry part a of x. 相似文献
12.
QiaoLingXIA YiBingSHEN 《数学学报(英文版)》2004,20(6):1029-1046
In this paper, we reformulate the Euler-Lagrange equations of Willmore surfaces in S^n as the flatness of a family of certain loop algebra-valued 1-forms. Therefore we can give the Weierstrass type representation of conformal Willmore surfaces. We also discuss the relations between conformal Willmore surfaces in S^n and minimal surfaces in constant curvature spaces S^n, R^n, H^n, and prove that some special Willmore surfaces can be derived from minimal surfaces in S^n, R^n, H^n. 相似文献
13.
Functions whose translates span L
p
(R) are called L
p-cyclic functions. For a fixed
p \memb [1, \infty], we construct Schwartz-class functions which are L
r
-cyclic for r > p and not L
r
-
cyclic for r \le p. We then construct Schwartz-class functions which are L
r
-cyclic for r \ge p and
not L
r
-cyclic for r < p. The constructions differ for p \memb (1, 2) and p > 2. 相似文献
14.
<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-invariants of Riemannian foliations
Luis Sanguiao 《Annals of Global Analysis and Geometry》2008,33(3):271-292
For a Riemannian foliation on a closed manifold M, we define L
2-spectral sequence Betti numbers and spectral sequence Novikov–Shubin invariants. The spectral sequence of the lift of to the universal covering of M is used in the definitions. These invariants are natural extensions of the L
2-Betti numbers and the Novikov–Shubin invariants of differentiable manifolds. It is shown that these numbers are invariant
by foliated homotopy equivalences, and they are computed for several examples.
相似文献
15.
In this article we study the problem of extending Fourier
Multipliers on L
p
(T) to those on L
p
(R)
by taking convolution with a kernel, called a summability
kernel. We characterize the space of such kernels
for the cases p = 1 and p = 2. For other values of p we give a
necessary condition for a function to be a
summability kernel. For the case p = 1, we present
properties of measures which are transferred from M(T) to
M(R) by summability kernels. Furthermore it is
shown that every l
p
sequence can be extended to some
L
q
(R) multipliers for certain values of p and q. 相似文献
16.
We give a characterization of structurally stable diffeomorphisms by making use of the notion of L
p
-shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C
1-interior of the set of diffeomorphisms having L
p
-shadowing property. 相似文献
17.
In this paper, we get W
1,p
(R
n
)-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and
Tananka’s results.
Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural
Science Foundation of China. 相似文献
18.
We investigate R-bounded representations
, where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism
, we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.
Dedicated to the memory of H. H. Schaefer 相似文献
19.
Patrick LaVictoire 《Journal d'Analyse Mathématique》2011,113(1):241-263
We present a modified version of Buczolich and Mauldin’s proof that the sequence of square numbers is universally L
1-bad. We extend this result to a large class of sequences, including the dth powers and the set of primes. Furthermore, we show that any subsequence of the averages taken along these sequences is
also universally L
1-bad. 相似文献
20.
Vladimir V. Tkachuk 《Acta Mathematica Hungarica》2005,107(4):253-265
Summary We prove that, for any Tychonoff X, the space Cp(X) is K-analytic if and only if it has a compact cover {Kp: p } such that Kp subset Kq whenever p,q and p q. Applying this result we show that if Cp(X) is K-analytic then Cp(X) is K-analytic as well. We also establish that a space Cp(X) is K-analytic and Baire if and only if X is countable and discrete. 相似文献