共查询到20条相似文献,搜索用时 500 毫秒
1.
Turdebek N. Bekjan 《Journal of Functional Analysis》2008,254(9):2401-2418
Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L2(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations. 相似文献
2.
Ying Hu 《Journal of Functional Analysis》2008,254(5):1282-1306
We prove maximal ergodic inequalities for a sequence of operators and for their averages in the noncommutative Lp-space. We also obtain the corresponding individual ergodic theorems. Applying these results to actions of a free group on a von Neumann algebra, we get noncommutative analogues of maximal ergodic inequalities and pointwise ergodic theorems of Nevo-Stein. 相似文献
3.
Turdebek N. Bekjan Zeqian Chen Mathilde Perrin Zhi Yin 《Journal of Functional Analysis》2010,258(7):2483-2505
We prove that atomic decomposition for the Hardy spaces h1 and H1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales hp and bmo form interpolation scales with respect to both complex and real interpolations. 相似文献
4.
Wei HuangDi-Rong Chen 《Journal of Computational and Applied Mathematics》2011,235(17):5017-5023
In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with ?p-norm (1<p≤2) constraint. Gradient iterations with ?p-norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the ?2-norm convergence of sequence constructed by the constrained gradient iteration when p∈(1,2]. The performance of the method is testified by a numerical example. 相似文献
5.
We study the numerical index of absolute sums of Banach spaces, giving general conditions which imply that the numerical index of the sum is less or equal than the infimum of the numerical indices of the summands and we provide some examples where the equality holds covering the already known case of c0-, ?1- and ?∞-sums and giving as a new result the case of E-sums where E has the RNP and n(E)=1 (in particular for finite-dimensional E with n(E)=1). We also show that the numerical index of a Banach space Z which contains a dense union of increasing one-complemented subspaces is greater or equal than the limit superior of the numerical indices of those subspaces. Using these results, we give a detailed short proof of the already known fact that, for a fixed p, the numerical indices of all infinite-dimensional Lp(μ)-spaces coincide. 相似文献
6.
The inclusion relations between the Lp-Sobolev spaces and the modulation spaces is determined explicitly. As an application, mapping properties of unimodular Fourier multiplier eiα|D| between Lp-Sobolev spaces and modulation spaces are discussed. 相似文献
7.
Juan Carlos Ferrando 《Journal of Mathematical Analysis and Applications》2011,380(1):323-326
If (Σ,X) is a measurable space and X a Banach space we investigate the X-inheritance of copies of ?∞ in certain subspaces Δ(Σ,X) of bvca(Σ,X), the Banach space of all X-valued countable additive measures of bounded variation equipped with the variation norm. Among the consequences of our main theorem we get a theorem of J. Mendoza on the X-inheritance of copies of ?∞ in the Bochner space L1(μ,X) and other of the author on the X-inheritance of copies of ?∞ in bvca(Σ,X). 相似文献
8.
We propose least squares estimators of E(Y/X=x) for Y censored on the right by R and min(Y,R) left censored. We establish their convergence in the L2-norm. This work extends a known result in the context of right censoring. 相似文献
9.
Marija Miloševi? Svetlana Jankovi? 《Journal of Mathematical Analysis and Applications》2010,363(1):128-4451
The subject of this paper is an analytic approximate method for stochastic functional differential equations whose coefficients are functionals, sufficiently smooth in the sense of Fréchet derivatives. The approximate equations are defined on equidistant partitions of the time interval, and their coefficients are general Taylor expansions of the coefficients of the initial equation. It will be shown that the approximate solutions converge in the Lp-norm and with probability one to the solution of the initial equation, and also that the rate of convergence increases when degrees in Taylor expansions increase, analogously to real analysis. 相似文献
10.
We give an alternative proof of a theorem of Stein and Weiss: The distribution function of the Hilbert transform of a characteristic function of a set E only depends on the Lebesgue measure |E| of such a set. We exploit a rational change of variable of the type used by George Boole in his paper “On the comparison of transcendents, with certain applications to the theory of definite integrals” together with the observation that if two functions f and g have the same Lp norm in a range of exponents p1<p<p2 then their distribution functions coincide. 相似文献
11.
Ond?ej F.K. Kalenda 《Journal of Mathematical Analysis and Applications》2008,340(1):81-101
We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces. 相似文献
12.
Svetlana Jankovi? 《Journal of Mathematical Analysis and Applications》2006,320(1):230-245
In this paper we compare the solution of a general stochastic integrodifferential equation of the Ito type, with the solutions of a sequence of appropriate equations of the same type, whose coefficients are Taylor series of the coefficients of the original equation. The approximate solutions are defined on a partition of the time-interval. The rate of the closeness between the original and approximate solutions is measured in the sense of the Lp-norm, so that it decreases if the degrees of these Taylor series increase, analogously to real analysis. The convergence with probability one is also proved. 相似文献
13.
Lizheng Lu 《Journal of Computational and Applied Mathematics》2011,235(6):1557-1563
We present an iteration method for the polynomial approximation of rational Bézier curves. Starting with an initial Bézier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The Lp-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the Lp-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L1-error criterion are better than those obtained using the L2-error and L∞-error criteria. 相似文献
14.
Given a graph G and integers p,q,d1 and d2, with p>q, d2>d1?1, an L(d1,d2;p,q)-labeling of G is a function f:V(G)→{0,1,2,…,n} such that |f(u)−f(v)|?p if dG(u,v)?d1 and |f(u)−f(v)|?q if dG(u,v)?d2. A k-L(d1,d2;p,q)-labeling is an L(d1,d2;p,q)-labeling f such that maxv∈V(G)f(v)?k. The L(d1,d2;p,q)-labeling number ofG, denoted by , is the smallest number k such that G has a k-L(d1,d2;p,q)-labeling. In this paper, we give upper bounds and lower bounds of the L(d1,d2;p,q)-labeling number for general graphs and some special graphs. We also discuss the L(d1,d2;p,q)-labeling number of G, when G is a path, a power of a path, or Cartesian product of two paths. 相似文献
15.
Sjoerd Dirksen 《Journal of Mathematical Analysis and Applications》2010,370(1):200-223
We present an abstract approach to noncommutative stochastic integration in the context of a finite von Neumann algebra equipped with a normal, faithful, tracial state, with respect to processes with tensor or freely independent increments satisfying a stationarity condition, using a decoupling technique. We obtain necessary and sufficient conditions for stochastic integrability of Lp-processes with respect to such integrators. We apply the theory to stochastic integration with respect to Boson and free Brownian motion. 相似文献
16.
Tuomas Hytönen 《Journal of Functional Analysis》2008,254(3):675-726
Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X -valued functions on Rn. We characterize Kato's square root estimates and the H∞-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp space. To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case X=C, we get a new approach to the Lp theory of square roots of elliptic operators, as well as an Lp version of Carleson's inequality. 相似文献
17.
Lizheng Lu 《Journal of Computational and Applied Mathematics》2009,231(1):412-422
We present a simple method for degree reduction of tensor product Bézier surfaces with tangent plane continuity in L2-norm. Continuity constraints at the four corners of surfaces are considered, so that the boundary curves preserve endpoints continuity of any order α. We obtain matrix representations for the control points of the degree reduced surfaces by the least-squares method. A simple optimization scheme that minimizes the perturbations of some related control points is proposed, and the surface patches after adjustment are C∞ continuous in the interior and G1 continuous at the common boundaries. We show that this scheme is applicable to surface patches defined on chessboard-like domains. 相似文献
18.
F. Rambla 《Journal of Mathematical Analysis and Applications》2006,317(2):659-667
We prove that if the one-point compactification of a locally compact, noncompact Hausdorff space L is the topological space called pseudoarc, then C0(L,C) is almost transitive. We also obtain two necessary conditions on a metrizable locally compact Hausdorff space L for C0(L) being almost transitive. 相似文献
19.
Franz Luef 《Journal of Functional Analysis》2009,257(6):1921-93
In the present investigation we link noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. We are therefore in the position to invoke modern methods of operator algebras, e.g. topological stable rank of Banach algebras, to display the deeper properties of Gabor frames. Furthermore, we are able to extend results due to Connes and Rieffel on projective modules over noncommutative tori to Banach algebras, which arise in a natural manner in Gabor analysis. The main goal of this investigation is twofold: (i) an interpretation of projective modules over noncommutative tori in terms of Gabor analysis and (ii) to show that the Morita-Rieffel equivalence between noncommutative tori is the natural framework for the duality theory of Gabor frames. More concretely, we interpret generators of projective modules over noncommutative tori as the Gabor atoms of multi-window Gabor frames for modulation spaces. Moreover, we show that this implies the existence of good multi-window Gabor frames for modulation spaces with Gabor atoms in e.g. Feichtinger's algebra or in Schwartz space. 相似文献
20.
Tomasz Kubiak 《Fuzzy Sets and Systems》2011,182(1):21-36
This paper is a sequel to the 1995 paper On L-Tychonoff spaces. The embedding theorem for L-topological spaces is shown to hold true for L an arbitrary complete lattice without imposing any order reversing involution (·)′ on L. Some results on completely L-regular spaces and on L-Tychonoff spaces, which have previously been known to hold true for (L,′) a frame, are exhibited as ones holding for (L,′) a meet-continuous lattice. For such a lattice an insertion theorem for completely L-regular spaces is given. Some weak forms of separating families of maps are discussed. We also clarify the dependence between the sub-T0 separation axiom of Liu and the L-T0 separation axiom of Rodabaugh. 相似文献