共查询到20条相似文献,搜索用时 703 毫秒
1.
H. Movahedi-Lankarani R. Wells 《Journal of Mathematical Analysis and Applications》2003,285(1):299-320
The C1-Weierstrass approximation theorem is proved for any compact subset X of a Hilbert space . The same theorem is also proved for Whitney 1-jets on X when X satisfies the following further condition: There exist finite dimensional linear subspaces such that ?n?1Hn is dense in and πn(X)=X∩Hn for each n?1. Here, is the orthogonal projection. It is also shown that when X is compact convex with and satisfies the above condition, then C1(X) is complete if and only if the C1-Whitney extension theorem holds for X. Finally, for compact subsets of , an extension of the C1-Weierstrass approximation theorem is proved for C1 maps with compact derivatives. 相似文献
2.
Jorge Antezana Demetrio Stojanoff 《Journal of Mathematical Analysis and Applications》2007,331(1):297-307
Let A be a C∗-algebra and be a positive unital map. Then, for a convex function defined on some open interval and a self-adjoint element a∈A whose spectrum lies in I, we obtain a Jensen's-type inequality f(?(a))??(f(a)) where ? denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered. 相似文献
3.
Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist x∗∈F(T) and a strictly increasing function , Φ(0)=0 such that for all x∈K, there exists j(x−x∗)∈J(x−x∗) such that
〈Tx−x∗,j(x−x∗)〉?‖x−x∗‖2−Φ(‖x−x∗‖). 相似文献
4.
Quoc-Phong Vu 《Journal of Mathematical Analysis and Applications》2007,334(1):487-501
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtx∈D(B)). For a closed subset Λ⊂R, we prove that the following properties (i) and (ii) are equivalent: (i) for every function f∈AP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution u∈AP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λ∈Λ and . 相似文献
5.
Chi-Wai Leung 《Journal of Mathematical Analysis and Applications》2006,322(2):699-711
In this article, we define a natural Banach ∗-algebra for a C∗-dynamical system (A,G,α) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is ∗-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and ∗-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press]. 相似文献
6.
Bertrand Lemaire 《Discrete Mathematics》2009,309(12):3793-3810
In this paper, we study the binary relations R on a nonempty N∗-set A which are h-independent and h-positive (cf. the introduction below). They are called homothetic positive orders. Denote by B the set of intervals of R having the form [r,+∞[ with 0<r≤+∞ or ]q,∞[ with q∈Q≥0. It is a Q>0-set endowed with a binary relation > extending the usual one on R>0 (identified with a subset of B via the map r?[r,+∞[). We first prove that there exists a unique map ΦR:A×A→B such that (for all and all ) we have Φ(mx,ny)=mn−1⋅Φ(x,y) and . Then we give a characterization of the homothetic positive orders R on A such that there exist two morphisms of N∗-sets satisfying . They are called generalized homothetic biorders. Moreover, if we impose some natural conditions on the sets u1(A) and u2(A), the representation (u1,u2) is “uniquely” determined by R. For a generalized homothetic biorder R on A, the binary relation R1 on A defined by is a generalized homothetic weak order; i.e. there exists a morphism of N∗-sets u:A→B such that (for all ) we have . As we did in [B. Lemaire, M. Le Menestrel, Homothetic interval orders, Discrete Math. 306 (2006) 1669-1683] for homothetic interval orders, we also write “the” representation (u1,u2) of R in terms of u and a twisting factor. 相似文献
7.
We study the bifurcation diagrams of classical positive solutions u with ‖u‖∞∈(0,∞) of the p-Laplacian Dirichlet problem
8.
Surjit Singh Khurana 《Journal of Mathematical Analysis and Applications》2009,350(1):290-293
Let X be a completely regular Hausdorff space, E Hausdorff a quasi-complete locally convex space and Cb(X,E) all E-valued bounded continuous functions on X with strict topologies βt, , . We prove that a linear continuous mapping T:Cb(X,E)→E arises from a scalar measure μ∈(Cb′(X),βz)(z=t,∞,τ) if and only if g(T(f))=0 whenever g○f=0 for any f∈Cb(X,E), g∈E′. 相似文献
9.
O. Blasco J.M. Calabuig T. Signes 《Journal of Mathematical Analysis and Applications》2008,348(1):150-164
Given three Banach spaces X, Y and Z and a bounded bilinear map , a sequence x=n(xn)⊆X is called B-absolutely summable if is finite for any y∈Y. Connections of this space with are presented. A sequence x=n(xn)⊆X is called B-unconditionally summable if is finite for any y∈Y and z∗∈Z∗ and for any M⊆N there exists xM∈X for which ∑n∈M〈B(xn,y),z∗〉=〈B(xM,y),z∗〉 for all y∈Y and z∗∈Z∗. A bilinear version of Orlicz-Pettis theorem is given in this setting and some applications are presented. 相似文献
10.
The purpose of this paper is to investigate when a weight ? on a partial O∗-algebra is a trace weighted by a positive self-adjoint operator Ω, that is, whenever s.t. X†∈L(X) and ?(X†□X)<∞. It is shown that if contains the inverse N of a positive compact operator such that the weak multiplication N□N is defined, then every weight ? on satisfying ?(N□N)<∞ is a trace weighted by some positive trace operator. 相似文献
11.
Bojan Magajna 《Journal of Mathematical Analysis and Applications》2008,342(2):1481-1484
A unital C∗-algebra A is weakly central if and only if for every x∈A there exists a sequence of elementary unital completely positive maps αn on A such that the sequence (αn(x)) converges to a central element. 相似文献
12.
Sanja Varošanec 《Journal of Mathematical Analysis and Applications》2007,326(1):303-311
We introduce a class of h-convex functions which generalize convex, s-convex, Godunova-Levin functions and P-functions. Namely, the h-convex function is defined as a non-negative function which satisfies f(αx+(1−α)y)?h(α)f(x)+h(1−α)f(y), where h is a non-negative function, α∈(0,1) and x,y∈J. Some properties of h-convex functions are discussed. Also, the Schur-type inequality is given. 相似文献
13.
Mohammad Javaheri 《Journal of Mathematical Analysis and Applications》2010,361(2):332-337
Let γ:[0,1]→2[0,1] be a continuous curve such that γ(0)=(0,0), γ(1)=(1,1), and γ(t)∈2(0,1) for all t∈(0,1). We prove that, for each n∈N, there exists a sequence of points Ai, 0?i?n+1, on γ such that A0=(0,0), An+1=(1,1), and the sequences and , 0?i?n, are positive and the same up to order, where π1, π2 are projections on the axes. 相似文献
14.
Najla A. Altwaijry 《Journal of Functional Analysis》2008,254(11):2866-2892
The Banach-Lie algebra L(A) of multiplication operators on the JB∗-triple A is introduced and it is shown that the hermitian part Lh(A) of L(A) is a unital GM-space the base of the dual cone in the dual GL-space ∗(Lh(A)) of which is affine isomorphic and weak∗-homeomorphic to the state space of L(A). In the case in which A is a JBW∗-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space Lh(A) satisfy
0?D(u,u)+D(v,v)?idA, 相似文献
15.
Zhihua Ren 《Journal of Mathematical Analysis and Applications》2003,284(1):118-126
In this paper we study smooth classification of hyperbolic vector fields based on their linear approximations only and obtain the following. On Rn, n?5, with only two kinds of exceptions, any two hyperbolic vector fields with generic nonlinear parts and where Ai are n×n matrices, are C1 conjugate to each other if and only if A1 and A2 are strictly similar, and they are C1 orbitally equivalent if and only if A1 and A2 are similar. 相似文献
16.
Wojciech Jab?oński 《Journal of Mathematical Analysis and Applications》2005,312(2):527-534
Assume that and are uniformly continuous functions, where D1,D2⊂X are nonempty open and arc-connected subsets of a real normed space X. We prove that then either f and g are affine functions, that is f(x)=x∗(x)+a and g(x)=x∗(x)+b with some x∗∈X∗ and a,b∈R or the algebraic sum of graphs of functions f and g has a nonempty interior in a product space X×R treated as a normed space with a norm . 相似文献
17.
Danilo Royer 《Journal of Mathematical Analysis and Applications》2006,323(1):33-41
Given a local homeomorphism where U⊆X is clopen and X is a compact and Hausdorff topological space, we obtain the possible transfer operators Lρ which may occur for given by α(f)=f○σ. We obtain examples of partial dynamical systems (XA,σA) such that the construction of the covariance algebra C∗(XA,σA), proposed by B.K. Kwasniewski, and the crossed product by a partial endomorphism O(XA,α,L), recently introduced by the author and R. Exel, associated to this system are not equivalent, in the sense that there does not exist an invertible function ρ∈C(U) such that O(XA,α,Lρ)≅C∗(XA,σA). 相似文献
18.
Mohamed Ali Toumi Nedra Toumi 《Journal of Mathematical Analysis and Applications》2006,324(2):1178-1194
Let A and B be two Archimedean vector lattices and let be a lattice homomorphism. We call that T is laterally closed if T(D) is a maximal orthogonal system in the band generated by T(A) in B, for each maximal orthogonal system D of A. In this paper we prove that any laterally closed lattice homomorphism T of an Archimedean vector lattice A with universal completion Au into a universally complete vector lattice B can be extended to a lattice homomorphism of Au into B, which is an improvement of a result of M. Duhoux and M. Meyer [M. Duhoux and M. Meyer, Extended orthomorphisms and lateral completion of Archimedean Riesz spaces, Ann. Soc. Sci. Bruxelles 98 (1984) 3-18], who established it for the order continuous lattice homomorphism case. Moreover, if in addition Au and B are with point separating order duals ′(Au) and B′ respectively, then the laterally closedness property becomes a necessary and sufficient condition for any lattice homomorphism to have a similar extension to the whole Au. As an application, we give a new representation theorem for laterally closed d-algebras from which we infer the existence of d-algebra multiplications on the universal completions of d-algebras. 相似文献
19.
Lajos Molnár 《Journal of Mathematical Analysis and Applications》2007,327(1):302-309
Let H be a Hilbert space and let A and B be standard ∗-operator algebras on H. Denote by As and Bs the set of all self-adjoint operators in A and B, respectively. Assume that and are surjective maps such that M(AM∗(B)A)=M(A)BM(A) and M∗(BM(A)B)=M∗(B)AM∗(B) for every pair A∈As, B∈Bs. Then there exist an invertible bounded linear or conjugate-linear operator and a constant c∈{−1,1} such that M(A)=cTAT∗, A∈As, and M∗(B)=cT∗BT, B∈Bs. 相似文献