共查询到20条相似文献,搜索用时 31 毫秒
1.
Ricardo del Campo Antonio Fernández Fernando Mayoral Francisco Naranjo Enrique A. Sánchez-Pérez 《数学学报(英文版)》2011,27(1):119-134
Let (Ω, Σ) be a measurable space and m 0: Σ → X 0 and m 1: Σ → X 1 be positive vector measures with values in the Banach Köthe function spaces X 0 and X 1. If 0 < α < 1, we define a new vector measure [m 0, m 1] α with values in the Calderón lattice interpolation space X 0 1?ga X 1 α and we analyze the space of integrable functions with respect to measure [m 0, m 1] α in order to prove suitable extensions of the classical Stein-Weiss formulas that hold for the complex interpolation of L p -spaces. Since each p-convex order continuous Köthe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces. 相似文献
2.
We consider (in general noncoercive) mixed problems in a bounded domain D in ? n for a second-order elliptic partial differential operator A(x, ?). It is assumed that the operator is written in divergent form in D, the boundary operator B(x, ?) is the restriction of a linear combination of the function and its derivatives to ?D and the boundary of D is a Lipschitz surface. We separate a closed set Y ? ?D and control the growth of solutions near Y. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, where the weight is a power of the distance to the singular set Y. Finally, we prove the completeness of the root functions associated with L.The article consists of two parts. The first part published in the present paper, is devoted to exposing the theory of the special weighted Sobolev–Slobodetskii? spaces in Lipschitz domains. We obtain theorems on the properties of these spaces; namely, theorems on the interpolation of these spaces, embedding theorems, and theorems about traces. We also study the properties of the weighted spaces defined by some (in general) noncoercive forms. 相似文献
3.
Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic.Then we prove that all unit spheres of the Lebesgue–Bochner function spaces L_p(μ, X) and L_q(μ, Y)are mutually uniformly homeomorphic where 1 ≤ p, q ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space L_p(μ, X), 1 ≤ p ∞,also has Property H. 相似文献
4.
For a Tychonoff space X, we obtain a criterion of the σ-countable compactness of the space of continuous functions C(X) with the set-open topology. In particular, for the class of extremally disconnected spaces X, we prove that the space C λ(X) is σ-countably compact if and only if X is a pseudocompact space, the set X(P) of all P-points of the space X is dense in X, and the family λ consists of finite subsets of the set X(P). 相似文献
5.
In the theory of operators on a Riesz space (vector lattice), an important result states that the Riesz homomorphisms (lattice homomorphisms) on C(X) are exactly the weighted composition operators. We extend this result to Riesz* homomorphisms on order dense subspaces of C(X). On those subspace we consider and compare various classes of operators that extend the notion of a Riesz homomorphism. Furthermore, using the weighted composition structure of Riesz* homomorphisms we obtain several results concerning bijective Riesz* homomorphisms. In particular, we characterize the automorphism group for order dense subspaces of C(X). Lastly, we develop a similar theory for Riesz* homomorphisms on subspace of \(C_0(X)\), for a locally compact Hausdorff space X, and apply it to smooth manifolds and Sobolev spaces. 相似文献
6.
Ofelia T. Alas Lucia R. Junqueira Jan van Mill Vladimir V. Tkachuk Richard G. Wilson 《Central European Journal of Mathematics》2011,9(3):603-615
For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ? X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω 1-monolithic compact space X, if C p (X)is star countable then it is Lindelöf. 相似文献
7.
Let θ ∈ (0, 1), λ ∈ [0, 1) and p, p 0, p 1 ∈ (1,∞] be such that (1 ? θ)/p 0 + θ/p 1 = 1/p, and let φ, φ0, φ1 be some admissible functions such that φ, φ0 p/p0 and φ1 p/p1 are equivalent. We first prove that, via the ± interpolation method, the interpolation L φ0 p0),λ (X), L φ1 p1), λ (X), θ> of two generalized grand Morrey spaces on a quasi-metric measure space X is the generalized grand Morrey space L φ p),λ (X). Then, by using block functions, we also find a predual space of the generalized grand Morrey space. These results are new even for generalized grand Lebesgue spaces. 相似文献
8.
Viorel Vâjâitu 《Czechoslovak Mathematical Journal》2016,66(2):493-509
We consider a convexity notion for complex spaces X with respect to a holomorphic line bundle L over X. This definition has been introduced by Grauert and, when L is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if H0(X,L) separates each point of X, then X can be realized as a Riemann domain over the complex projective space Pn, where n is the complex dimension of X and L is the pull-back of O(1). 相似文献
9.
It was proved by R. Gomory and T. Hu in 1961 that, for every finite nonempty ultrametric space (X, d), the inequaliy \( \left| {\mathrm{Sp}(X)} \right|\leq \left| X \right|-1 \), where Sp(X) = {d(x, y) : x, y ∈ X, x ≠ y} , holds. We characterize the spaces X for which the equality is attained by the structural properties of some graphs and show that the set of isometric types of such X is dense in the Gromov–Hausdorff space of the isometric types of compact ultrametric spaces. 相似文献
10.
The spaces X in which every prime z°-ideal of C(X) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X, such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime z°-ideal in C(X) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C(X) a z°-ideal? When is every nonregular (prime) z-ideal in C(X) a z°-ideal? For instance, we show that every nonregular prime ideal of C(X) is a z°-ideal if and only if X is a ?-space (a space in which the boundary of any zeroset is contained in a zeroset with empty interior). 相似文献
11.
Mikael de la Salle 《Israel Journal of Mathematics》2016,211(1):105-145
We prove that SL(3, ?) has Strong Banach property (T) in Lafforgue’s sense with respect to the Banach spaces that are θ > 0 interpolation spaces (for the complex interpolation method) between an arbitrary Banach space and a Banach space with sufficiently good type and cotype. As a consequence, every action of SL(3, ?) or its lattices by affine isometries on such a Banach space X has a fixed point, and the expanders contructed from SL(3, ?) do not admit a coarse embedding into X. We also prove a quantitative decay of matrix coefficients (Howe-Moore property) for representations with small exponential growth of SL(3, ?) on X. 相似文献
12.
Igor I. Skrypnik 《Israel Journal of Mathematics》2016,212(1):163-188
We study the well-posedness of the third-order degenerate differential equation \(\left( {{P_3}} \right):\alpha {\left( {Mu} \right)^{\prime \prime \prime }}\left( t \right) + {\left( {Mu} \right)^{\prime \prime }}\left( t \right) = \beta Au\left( t \right) + f\left( t \right)\), (t ∈ [0, 2p]) with periodic boundary conditions \(Mu\left( 0 \right) = Mu\left( {2\pi } \right),\;Mu'\left( 0 \right) = Mu'\left( {2\pi } \right),\;Mu''\left( 0 \right) = Mu''\left( {2\pi } \right)\), in periodic Lebesgue–Bochner spaces Lp(T,X), periodic Besov spaces Bp,qs(T,X) and periodic Triebel–Lizorkin spaces Fp,qs(T,X), where A, B and M are closed linear operators on a Banach space X satisfying D(A) \( \cap \)D(B) ? D(M) and α, β, γ ∈ R. Using known operator-valued Fourier multiplier theorems, we completely characterize the well-posedness of (P3) in the above three function spaces. 相似文献
13.
I. Ghenciu 《Acta Mathematica Hungarica》2018,155(2):439-457
The p-Gelfand–Phillips property (1 \({\leq}\) p < ∞) is studied in spaces of operators. Dunford–Pettis type like sets are studied in Banach spaces. We discuss Banach spaces X with the property that every p-convergent operator T:X \({\rightarrow}\) Y is weakly compact, for every Banach space Y. 相似文献
14.
Let (X, d, μ) be a metric measure space with doubling property. The Hardy spaces associated with operators L were introduced and studied by many authors. All these spaces, however, were first defined by L 2(X) functions and finally the Hardy spaces were formally defined by the closure of these subspaces of L 2(X) with respect to Hardy spaces norms. A natural and interesting question in this context is to characterize the closure. The purpose of this paper is to answer this question. More precisely, we will introduce \({CMO}_{L}^{p}(X)\), the Carleson measure spaces associated with operators L, and characterize the Hardy spaces associated with operators L via \(({CMO}_{L}^{p}(X))'\), the distributions of \({CMO}_{L}^{p}(X)\). 相似文献
15.
A closed subspace H of a symmetric space X on [0, 1] is said to be strongly embedded in X if in H the convergence in X-norm is equivalent to the convergence in measure. We study symmetric spaces X with the property that all their reflexive subspaces are strongly embedded in X. We prove that it is the case for all spaces, which satisfy an analogue of the classical Dunford–Pettis theorem on relatively weakly compact subsets in L1. At the same time the converse assertion fails for a broad class of separableMarcinkiewicz spaces. 相似文献
16.
Let X be a partially ordered real Banach space, let a,b∈X with a≤b. Let φ be a bounded linear functional on X. We say that X satisfies the box-optimization property (or X is a BOP space) if the box-constrained linear program: max 〈φ,x〉, s.t. a≤x≤b, has an optimal solution for any φ,a and b. Such problems arise naturally in solving a class of problems known as interval linear programs. BOP spaces were introduced (in a different language) and systematically studied in the first author’s doctoral thesis. In this paper, we identify new classes of Banach spaces that are BOP spaces. We present also sufficient conditions under which answers are in the affirmative for the following questions:
相似文献
- (i)When is a closed subspace of a BOP space a BOP space?
- (ii)When is the range of a bounded linear map a BOP space?
- (iii)Is the quotient space of a BOP space a BOP space?
17.
A. M. Jerbashian J. Pejendino 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(4):212-222
Some extensions of the results of the first author related with the Hilbert spaces A ω,0 2 of functions holomorphic in the half–plane are proved. Some new Hilbert spaces A ω 2 of Dirichlet type are introduced, which are included in the Hardy space H2 over the half–plane. Several results on representations, boundary properties, isometry, interpolation, biorthogonal systems and bases are obtained for the spaces A ω 2 ? H2. 相似文献
18.
E. S. Zhukovskiy 《Siberian Mathematical Journal》2018,59(6):1063-1072
The recent articles of Arutyunov and Greshnov extend the Banach and Hadler Fixed-Point Theorems and the Arutyunov Coincidence-Point Theorem to the mappings of (q1, q2)-quasimetric spaces. This article addresses similar questions for f-quasimetric spaces.Given a function f: R +2 → R+ with f(r1, r2) → 0 as (r1, r2) → (0, 0), an f-quasimetric space is a nonempty set X with a possibly asymmetric distance function ρ: X2 → R+ satisfying the f-triangle inequality: ρ(x, z) ≤ f(ρ(x, y), ρ(y, z)) for x, y, z ∈ X. We extend the Banach Contraction Mapping Principle, as well as Krasnoselskii’s and Browder’s Theorems on generalized contractions, to mappings of f-quasimetric spaces. 相似文献
19.
We give an example of an infinite metrizable space X such that the space Cp(X), of continuous real-valued functions on X endowed with the pointwise topology, is not homeomorphic to its own square Cp(X) × Cp(X). The space X is a zero-dimensional subspace of the real line. Our result answers a long-standing open question in the theory of function spaces posed by A. V. Arhangel’skii. 相似文献
20.
Hana Krulišová 《Czechoslovak Mathematical Journal》2017,67(4):937-951
A Banach space X has Pe?czyński’s property (V) if for every Banach space Y every unconditionally converging operator T: X → Y is weakly compact. H.Pfitzner proved that C*-algebras have Pe?czyński’s property (V). In the preprint (Kruli?ová, (2015)) the author explores possible quantifications of the property (V) and shows that C(K) spaces for a compact Hausdorff space K enjoy a quantitative version of the property (V). In this paper we generalize this result by quantifying Pfitzner’s theorem. Moreover, we prove that in dual Banach spaces a quantitative version of the property (V) implies a quantitative version of the Grothendieck property. 相似文献