共查询到20条相似文献,搜索用时 218 毫秒
1.
Let E be a Banach lattice and F a Banach space. A bounded linear operator T:E→F is an isomorphism on the positive cone of E if and only if T∗ is almost surjective. A dual version of this theorem holds also. A bounded linear operator T:F→E is almost surjective if and only if T∗ is an isomorphism on the positive cone of F∗. 相似文献
2.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
3.
We show that if T:X→X is a continuous linear operator on an F-space X≠{0}, then the set of frequently hypercyclic vectors of T is of first category in X, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T:X→X is a bounded linear operator on a Banach space X≠{0} and if T is frequently hypercyclic (or, more generally, syndetically transitive), then the T∗-orbit of every non-zero element of X∗ is bounded away from 0, and in particular T∗ is not hypercyclic. 相似文献
4.
We prove that θ∗ as previously defined [Int. J. Contemp. Math. Sci. 5 (2010) 721] is the smallest equivalence relation such that the quotient structure R/θ∗ is a commutative fundamental ring. We also investigate some properties with respect to the commutative fundamental relation θ∗ on a hyperring R. 相似文献
5.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are bounded strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
6.
For a non-degenerate convex subset Y of the n -dimensional Euclidean space Rn, let F(Y) be the family of all fuzzy sets of Rn which are upper semicontinuous, fuzzy convex and normal with compact supports contained in Y . We show that the space F(Y) with the topology of sendograph metric is homeomorphic to the separable Hilbert space ?2 if Y is compact; and the space F(Rn) is also homeomorphic to ?2. 相似文献
7.
Roe algebras are C?-algebras built using large scale (or ‘coarse’) aspects of a metric space (X,d). In the special case that X=Γ is a finitely generated group and d is a word metric, the simplest Roe algebra associated to (Γ,d) is isomorphic to the crossed product C?-algebra l∞(Γ)?rΓ. 相似文献
8.
Michel Mandjes Petteri Mannersalo Ilkka Norros Miranda van Uitert 《Stochastic Processes and their Applications》2006
Consider events of the form {Zs≥ζ(s),s∈S}, where Z is a continuous Gaussian process with stationary increments, ζ is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S⊂R is compact. The main problem considered in this paper is identifying the function β∗∈R satisfying β∗(s)≥ζ(s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s for s∈[0,1] and Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process. 相似文献
9.
A net (xα) in a vector lattice X is said to be unbounded order convergent (or uo-convergent, for short) to x∈X if the net (|xα−x|∧y) converges to 0 in order for all y∈X+. In this paper, we study unbounded order convergence in dual spaces of Banach lattices. Let X be a Banach lattice. We prove that every norm bounded uo-convergent net in X? is w?-convergent iff X has order continuous norm, and that every w?-convergent net in X? is uo-convergent iff X is atomic with order continuous norm. We also characterize among σ -order complete Banach lattices the spaces in whose dual space every simultaneously uo- and w?-convergent sequence converges weakly/in norm. 相似文献
10.
11.
In this paper, we introduce the metric dG on a G -metric space (X,G) and use this notion to show that many contraction conditions for maps on the G -metric space (X,G) reduce to certain contraction conditions for maps on the metric space (X,dG). As applications, the proofs of many fixed point theorems for maps on the G -metric space (X,G) may be simplified, and many fixed point theorems for maps on the G -metric space (X,G) are direct consequences of preceding results for maps on the metric space (X,dG). 相似文献
12.
Let P(D) be a nonnegative homogeneous elliptic operator of order 2m with real constant coefficients on Rn and V be a suitable real measurable function. In this paper, we are mainly devoted to establish the Gaussian upper bound for Schrödinger type semigroup e−tH generated by H=P(D)+V with Kato type perturbing potential V , which naturally generalizes the classical result for Schrödinger semigroup e−t(Δ+V) as V∈K2(Rn), the famous Kato potential class. Our proof significantly depends on the analyticity of the free semigroup e−tP(D) on L1(Rn). As a consequence of the Gaussian upper bound, the Lp-spectral independence of H is concluded. 相似文献
13.
14.
We prove various Hardy-type and uncertainty inequalities on a stratified Lie group G . In particular, we show that the operators Tα:f?|⋅|−αL−α/2f, where |⋅| is a homogeneous norm, 0<α<Q/p, and L is the sub-Laplacian, are bounded on the Lebesgue space Lp(G). As consequences, we estimate the norms of these operators sufficiently precisely to be able to differentiate and prove a logarithmic uncertainty inequality. We also deduce a general version of the Heisenberg–Pauli–Weyl inequality, relating the Lp norm of a function f to the Lq norm of |⋅|βf and the Lr norm of Lδ/2f. 相似文献
15.
We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (−Δ)su=g in Ω , u≡0 in Rn\Ω, for some s∈(0,1) and g∈L∞(Ω), then u is Cs(Rn) and u/δs|Ω is Cα up to the boundary ∂Ω for some α∈(0,1), where δ(x)=dist(x,∂Ω). For this, we develop a fractional analog of the Krylov boundary Harnack method. 相似文献
16.
Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) [2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) [8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) [5]. 相似文献
17.
Recently, Alfakih and Ye (2013) [4] proved that if an r -dimensional bar framework (G,p) on n?r+2 nodes in general position in Rr admits a positive semidefinite stress matrix with rank n−r−1, then (G,p) is universally rigid. In this paper, we generalize this result in two directions. First, we extend this result to tensegrity frameworks. Second, we replace the general position assumption by the weaker assumption that in configuration p, each point and its neighbors in G affinely span Rr. 相似文献
18.
19.
20.
This paper treats some variational principles for solutions of inhomogeneous p -Laplacian boundary value problems on exterior regions U?RN with dimension N?3. Existence-uniqueness results when p∈(1,N) are provided in a space E1,p(U) of functions that contains W1,p(U). Functions in E1,p(U) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an Lp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained. 相似文献