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1.
The final aim of this work is to prove the Central Limit Theorem described in the motivations given below. The key for that is a Resolvant estimate, of the type of Theorem 1.1 in [21], adapted for the Parabolic Green function G(X, Y) which is the heat diffusion kernel in some domain Ω in time-space: i.e. we must estimate ${\int_{\Omega}\nabla_{Y}G(X, Y)\nabla_{Y}^{2}G(Y,Z)\;dY}The final aim of this work is to prove the Central Limit Theorem described in the motivations given below. The key for that is a Resolvant estimate, of the type of Theorem 1.1 in [21], adapted for the Parabolic Green function G(X, Y) which is the heat diffusion kernel in some domain Ω in time-space: i.e. we must estimate òW?YG(X, Y)?Y2G(Y,Z)  dY{\int_{\Omega}\nabla_{Y}G(X, Y)\nabla_{Y}^{2}G(Y,Z)\;dY}. Exactly as the estimate in [21] is based on [10] our estimate here is based on the main Theorem of this paper. This main theorem refers to rough singular integrals on the Gaussian potential on ∂Ω.  相似文献   

2.
We prove here a theorem, which generalizes Grauert's comparison theorem ([4], Hauptsatz IIa; cf. also Knorr [7], Vergleichssatz) and which is an analogue of a Grothéndieck's result in Algebraic Geometry ([6], Chap. III., 4.1.5). The proof makes essential use of a coherence theorem for sheaves of polynomials: Let X,Y be complex spaces, : XY a proper holomorphic map and T=(T1,...,TN) a system of indeterminates. Then, for everyO X[T] graded sheafm, all direct image sheaves Rq* m areY[T]-coherent. The proof is as in [2].

Diese Arbeit entstand während eines Aufenthalts des Verfassers am Fachbereich Mathematik der Universität Regensburg als Stipendiat der Alexander-von-Humboldt-Stiftung.  相似文献   

3.
Let X be a Banach space, let Y be its subspace, and let Г be an infinite set. We study the consequences of the assumption that an operator T embeds ?221E;(Г) into X isomorphically with T(c0(Г)) ⊂ Y. Under additional assumptions on T we prove the existence of isomorphic copies of c0ℵ0) in X/Y, and complemented copies ?(Г) in X/Y. In concrete cases we obtain a new information about the structure of X/Y. In particular, L∞[O,1]/C[O,1] contains a complemented copy of ?/c0, and some natural (lattice) quotients of real Orlicz and Marcinkiewicz spaces contain lattice-isometric and positively I-complemented copies of(real) ?/c0.  相似文献   

4.
Let X and Y Banach spaces. Two new properties of operator Banach spaces are introduced. We call these properties "boundedly closed" and "d-boundedly closed". Among other results, we prove the following one. Let U(X, Y){\cal U}(X, Y) an operator Banach space containing a complemented copy of c0. Then we have: 1) If U(X, Y){\cal U}(X, Y) is boundedly closed then Y contains a copy of c0. 2) If U(X, Y){\cal U}(X, Y) is d-boundedly closed, then X* or Y contains a copy of c0.  相似文献   

5.
We show that ifX is a Banach lattice containing no copy ofc 0 and ifZ is a subspace ofX isomorphic toL 1[0, 1] then (a)Z contains a subspaceZ 0 isomorphic toL 1 and complemented inX and (b)X contains a complemented sublattice isomorphic and lattice-isomorphic toL 1.  相似文献   

6.
Let X be a Banach space and Y a finite-dimensional subspace of X. Let P be a minimal projection of X onto Y. It is shown (Theorem 1.1) that under certain conditions there exist sequences of finite-dimensional “approximating subspaces” Xm and Ym of X with corresponding minimal projections Pm: XmYm, such that limm→∞ Pm = P. Moreover, a certain related sequence of projections imPm○πm: XY has cluster points in the strong operator topology, each of which is a minimal projection of X onto Y. When X = C[a, b] the result reduces to a theorem of [7.]. It is shown (Corollary 1.11) that the hypothesis of Theorem 1.1 holds in many important Banach spaces, including C[a, b], LP[a, b] and lP for 1 p < ∞, and c0, the space of sequences converging to zero in the sup norm.  相似文献   

7.
Let T be a locally compact Hausdorff space and let C 0(T) be the Banach space of all complex valued continuous functions vanishing at infinity in T, provided with the supremum norm. Let X be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of X-valued -additive Baire measures on T is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map u: C 0(T) X when c 0 X are obtained. The proof of the latter result is independent of the use of powerful results such as Theorem 6 of [6] or Theorem 3 (vii) of [13].  相似文献   

8.
Criteria for Orlicz spaces containing an isomorphic as well as an almost isometric complemented copy of l1 are given. The same is made for copies of l and c0 in Orlicz spaces and in the subspace of order continuous elements in Orlicz space, respectively. The Hahn-Banach theorem is not used in the constructions of the projections.  相似文献   

9.
In this paper we give two generalizations of a theorem of Beppo Levi ([1], p. 347, Formula (12)). This theorem affirms that, under certain conditions, the following assertion is true: where φ(x) is a function that verifies φ(0) > 0; f(x) is defined and bounded in the interval (a, b) and continuous in the point 0 with f(0) ≠ 0; f(x) and φ(x) are integrable functions in the interval [a, b]; c >, 0 and υ > 1. This problem was studied by Laplace [2], Darboux [3], Stieltjes [4], Lebesgue [5], Romanovsky [6], and Fowler [7]. The first generalization (Section 1, Theorem 1.2, Formula (1.35)) says that, under certain conditions, the following formula is valid: where φn(x) is a sequence of functions and Bn(a) designates the n-dimentional ball of radius a and center in the origin. The extension follows by Romanovsky's method. The absolute maximum of φ(x) in the extremes of the interval of definition is treated in the second generalization of the Theorem of Beppo Levi (Section 2, Theorem 2.2, Formulas (2.1), (2.2)). We note that Beppo Levi proves this assertion in the interior of the interval.  相似文献   

10.
By applying a main comparison theorem of Pucci and Serrin (2007) [2] we cover, for general equations of p-Laplace type, the open cases of Theorems B, D, E of Farina and Serrin (submitted for publication) [1] as described in Problems 2 and 3 of Section 12 of Farina and Serrin (submitted for publication) [1]. Moreover, we provide significant improvements of Theorem C and Theorem 5 of Farina and Serrin (submitted for publication) [1], the latter in the context of mean curvature type operators, see Theorem 1.3 and Theorems 5.2-5.4 below.Finally, Theorem 1.1 provides a new Liouville theorem outside the context of work in Farina and Serrin (submitted for publication) [1].  相似文献   

11.
Asymplectic integration of a Poisson manifold (M, Λ) is a symplectic groupoid (Γ,η) whichrealizes the given Poisson manifold, i.e. such that the space of units Γ0 with the induced Poisson structure Λ0 is isomorphic to (M, Λ). This notion was introduced by A. Weinstein in [28] in order to quantize Poisson manifolds by quantizing their symplectic integration. Any Poisson manifold can be integrated by alocal symplectic groupoid ([4], [13]) but already for regular Poisson manifolds there are obstructions to global integrability ([2], [6], [11], [17], [28]). The aim of this paper is to summarize all the known obstructions and present a sufficient topological condition for integrability of regular Poisson manifolds; we will indeed describe a concrete procedure for this integration. Further our criterion will provide necessary and sufficient if we require Γ to be Hausdorff, which is a suitable condition to proceed to Weinstein’s program of quantization. These integrability results may be interpreted as a generalization of the Cartan-Smith proof of Lie’s third theorem in the infinite dimensional case.

Recherche supportée par D.G.I.C.Y.T. Espagne (Proyecto PB90-0765) et Xunta de Galicia (Proxecto XUGA20704B90)  相似文献   

12.
We prove that any class VII surface with b2=1 has curves. This implies the “Global Spherical Shell conjecture” in the case b2=1: Any minimal class VII surface withb2=1 admits a global spherical shell, hence it is isomorphic to one of the surfaces in the known list. By the results in [LYZ], [Te1], which treat the case b2=0 and give complete proofs of Bogomolov’s theorem, one has a complete classification of all class VII-surfaces with b2∈{0,1}. The main idea of the proof is to show that a certain moduli space of PU(2)-instantons on a surface X with no curves (if such a surface existed) would contain a closed Riemann surface Y whose general points correspond to non-filtrable holomorphic bundles on X. Then we pass from a family of bundles on X parameterized by Y to a family of bundles on Y parameterized by X, and we use the algebraicity of Y to obtain a contradiction. The proof uses essentially techniques from Donaldson theory: compactness theorems for moduli spaces of PU(2)-instantons and the Kobayashi-Hitchin correspondence on surfaces.  相似文献   

13.
In this note we study some properties concerning certain copies of the classic Banach space c 0 in the Banach space of all bounded linear operators between a normed space X and a Banach space Y equipped with the norm of the uniform convergence of operators.  相似文献   

14.
In this paper, we construct maximally monotone operators that are not of Gossez’s dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Brønsted-Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC–functions will not always be a BC–function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce—in a uniform fashion—that every Banach space which contains an isomorphic copy of the James space \({\ensuremath{\mathbf{J}}}\) or its dual \({\ensuremath{\mathbf{J}}}^{\ast}\), or c 0 or its dual ?1, admits a non type (D) operator. The existence of non type (D) operators in spaces containing ?1 or c 0 has been proved recently by Bueno and Svaiter.  相似文献   

15.
Given Banach spaces X, Yand a compact Hausdorff space K, we use polymeasures to give necessary conditions for a multilinear operator from C(K, X) into Yto be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for Xto have the Schur property (resp. to contain no copy of c 0), and for Kto be scattered. This extends results concerning linear operators.  相似文献   

16.
We determine the smooth points of certain spaces of bounded operatorsL(X,Y), including the cases whereX andY arel p -orc 0-direct sums of finite dimensional Banach spaces or subspaces of the latter enjoying the metric compact approximation property. We also remark that the operators not attaining their norm are nowhere dense inL(X,Y) wheneverK(X,Y) is anM-ideal inL(X,Y).  相似文献   

17.
Let X and Y denote compact Hausdorff spaces and let K = R (real numbers) or C(complex numbers). C(X) and C(Y) denote the spaces of K-valued continuous functions on X and Y, respectively. A map H : C(X) C(Y) is separating if fg = 0 implies that HfHg = 0. Results about automatic continuity and the form of additive and linear separating maps have been developed in [1], [2], [3], [4], [5], [7], [8], and [10]. In this article similar results are developed for subadditive separating maps. We show (Theorem 5.11) that certain biseparating, subadditive bijections H are automatically continuous.  相似文献   

18.
In [5], it is proved that a bounded linear operator u, from a Banach space Y into an Lp(S, ν) factors through Lp1 (S, ν) for some p1 > 1, if Y* is of finite cotype; (S, ν) is a probability space for p = 0, and any measure space for 0 < p < 1. In this paper, we generalize this result to uv, where u : YLp(S, ν) and v : XY are linear operators such that v* is of finite Ka?in cotype. This result gives also a new proof of Grothendieck's theorem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

19.
Given an operator T : XY between Banach spaces, and a Banach lattice E consisting of measurable functions, we consider the point-wise extension of the operator to the vector-valued Banach lattices T E : E(X) → E(Y) given by T E (f)(ω) = T(f(ω)). It is proved that for any Banach lattice E which does not contain c 0, the operator T is an isomorphism on a subspace isomorphic to c 0 if and only if so is T E . An analogous result for invertible operators on subspaces isomorphic to 1 is also given.  相似文献   

20.
《Quaestiones Mathematicae》2013,36(4):509-517
Abstract

Suppose X and Y are FK spaces in which ? the span of the coordinate vectors (en) is dense. Let L(X,Y) denote the space of all matrices of the form Ei(T(ej)) as T ranges over all continuous linear operators from X into Y; here ei represents the ith coordinate vector and Ei represents the ith coordinate functional. Let M(L(X, Y)) denote the space of all matrices B such that (B(i,j)A(i,j)) is in L(X,Y) whenever A is in L(X,Y). In this paper we shall show how the summability properties of X and Y determine the extent of M(L(X,Y)) and conversely how the extent of M(L(X,Y)) determines the summability properties of both X and Y.  相似文献   

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