共查询到20条相似文献,搜索用时 46 毫秒
1.
Jer-Shyong Lin 《Linear algebra and its applications》2010,432(1):14-23
Let A be a prime ring of characteristic not 2, with center Z(A) and with involution *. Let S be the set of symmetric elements of A. Suppose that f:S→A is an additive map such that [f(x),f(y)]=[x,y] for all x,y∈S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ:S→Z(A) such that f(x)=x+μ(x) for all x∈S or f(x)=-x+μ(x) for all x∈S. 相似文献
2.
Let A⊂C(X) and B⊂C(Y) be uniform algebras with Choquet boundaries δA and δB. A map T:A→B is called norm-linear if ‖λTf+μTg‖=‖λf+μg‖; norm-additive, if ‖Tf+Tg‖=‖f+g‖, and norm-additive in modulus, if ‖|Tf|+|Tg|‖=‖|f|+|g|‖ for each λ,μ∈C and all algebra elements f and g. We show that for any norm-linear surjection T:A→B there exists a homeomorphism ψ:δA→δB such that |(Tf)(y)|=|f(ψ(y))| for every f∈A and y∈δB. Sufficient conditions for norm-additive and norm-linear surjections, not assumed a priori to be linear, or continuous, to be unital isometric algebra isomorphisms are given. We prove that any unital norm-linear surjection T for which T(i)=i, or which preserves the peripheral spectra of C-peaking functions of A, is a unital isometric algebra isomorphism. In particular, we show that if a linear operator between two uniform algebras, which is surjective and norm-preserving, is unital, or preserves the peripheral spectra of C-peaking functions, then it is automatically multiplicative and, in fact, an algebra isomorphism. 相似文献
3.
Svatoslav Staněk 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e153
The paper discusses the existence of positive and dead core solutions of the singular differential equation (?(u″))′=λf(t,u,u′,u″) satisfying the boundary conditions u(0)=A, u(T)=A, min{u(t):t∈[0,T]}=0. Here λ is a nonnegative parameter, A is a positive constant and the Carathéodory function f(t,x,y,z) is singular at the value 0 of its space variable y. 相似文献
4.
Jian YuDingtao Peng Shuwen Xiang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6326-6332
Let X be a nonempty, convex and compact subset of normed linear space E (respectively, let X be a nonempty, bounded, closed and convex subset of Banach space E and A be a nonempty, convex and compact subset of X) and f:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈X (respectively, x∗∈A) such that f(x∗,y)≥0 for all y∈X (respectively, f(x∗,y)≥0 for all y∈A) is studied with varying f (respectively, with both varying f and varying A). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point. 相似文献
5.
Janusz Brzd?k 《Journal of Mathematical Analysis and Applications》2011,381(1):299-307
Let C be a convex symmetric subset of a real Banach space F and K be a subgroup of the group (F,+). Let E be a real linear space, h:E→F, and h(x+y)−h(x)−h(y)∈K+C for x,y∈E. We prove that under some additional assumptions h can be represented in the form: h=A+γ+κ with an additive (or linear) A:E→F and some γ:E→C, κ:E→K. 相似文献
6.
José Luis Bravo Manuel Fernández 《Journal of Mathematical Analysis and Applications》2007,336(1):438-454
We study the structure induced by the number of periodic solutions on the set of differential equations x′=f(t,x) where f∈C3(R2) is T-periodic in t, fx3(t,x)<0 for every (t,x)∈R2, and f(t,x)→?∞ as x→∞, uniformly on t. We find that the set of differential equations with a singular periodic solution is a codimension-one submanifold, which divides the space into two components: equations with one periodic solution and equations with three periodic solutions. Moreover, the set of differential equations with exactly one periodic singular solution and no other periodic solution is a codimension-two submanifold. 相似文献
7.
Jiankui Li 《Linear algebra and its applications》2010,432(1):5-322
For a commutative subspace lattice L in a von Neumann algebra N and a bounded linear map f:N∩algL→B(H), we show that if Af(B)C=0 for all A,B,C∈N∩algL satisfying AB=BC=0, then f is a generalized derivation. For a unital C∗-algebra A, a unital Banach A-bimodule M, and a bounded linear map f:A→M, we prove that if f(A)B=0 for all A,B∈A with AB=0, then f is a left multiplier; as a consequence, every bounded local derivation from a C∗-algebra to a Banach A-bimodule is a derivation. We also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier. 相似文献
8.
Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),fk(y)}⊂(x,y) for some m,k∈N, then R(f)∩(x,y)≠∅; (2) Any isolated point of P(f) is also an isolated point of Ω(f); (3) If x∈Ω(f)−Ω(fn) for some n∈N, then x is an eventually periodic point. These generalize the corresponding results in W. Huang and X. Ye (2001) [9] and J. Xiong (1983, 1986) [17] and [19] on interval maps or tree maps. 相似文献
9.
The notion of a modular is introduced as follows. A (metric) modular on a set X is a function w:(0,∞)×X×X→[0,∞] satisfying, for all x,y,z∈X, the following three properties: x=y if and only if w(λ,x,y)=0 for all λ>0; w(λ,x,y)=w(λ,y,x) for all λ>0; w(λ+μ,x,y)≤w(λ,x,z)+w(μ,y,z) for all λ,μ>0. We show that, given x0∈X, the set Xw={x∈X:limλ→∞w(λ,x,x0)=0} is a metric space with metric , called a modular space. The modular w is said to be convex if (λ,x,y)?λw(λ,x,y) is also a modular on X. In this case Xw coincides with the set of all x∈X such that w(λ,x,x0)<∞ for some λ=λ(x)>0 and is metrizable by . Moreover, if or , then ; otherwise, the reverse inequalities hold. We develop the theory of metric spaces, generated by modulars, and extend the results by H. Nakano, J. Musielak, W. Orlicz, Ph. Turpin and others for modulars on linear spaces. 相似文献
10.
We say that a matrix R∈Cn×n is k-involutary if its minimal polynomial is xk-1 for some k?2, so Rk-1=R-1 and the eigenvalues of R are 1,ζ,ζ2,…,ζk-1, where ζ=e2πi/k. Let α,μ∈{0,1,…,k-1}. If R∈Cm×m, A∈Cm×n, S∈Cn×n and R and S are k-involutory, we say that A is (R,S,μ)-symmetric if RAS-1=ζμA, and A is (R,S,α,μ)-symmetric if RAS-α=ζμA.Let L be the class of m×n(R,S,μ)-symmetric matrices or the class of m×n(R,S,α,μ)-symmetric matrices. Given X∈Cn×t and B∈Cm×t, we characterize the matrices A in L that minimize ‖AX-B‖ (Frobenius norm), and, given an arbitrary W∈Cm×n, we find the unique matrix A∈L that minimizes both ‖AX-B‖ and ‖A-W‖. We also obtain necessary and sufficient conditions for existence of A∈L such that AX=B, and, assuming that the conditions are satisfied, characterize the set of all such A. 相似文献
11.
Kristopher Lee 《Journal of Mathematical Analysis and Applications》2011,375(1):108-117
Let A and B be uniform algebras on first-countable, compact Hausdorff spaces X and Y, respectively. For f∈A, the peripheral spectrum of f, denoted by σπ(f)={λ∈σ(f):|λ|=‖f‖}, is the set of spectral values of maximum modulus. A map T:A→B is weakly peripherally multiplicative if σπ(T(f)T(g))∩σπ(fg)≠∅ for all f,g∈A. We show that if T is a surjective, weakly peripherally multiplicative map, then T is a weighted composition operator, extending earlier results. Furthermore, if T1,T2:A→B are surjective mappings that satisfy σπ(T1(f)T2(g))∩σπ(fg)≠∅ for all f,g∈A, then T1(f)T2(1)=T1(1)T2(f) for all f∈A, and the map f?T1(f)T2(1) is an isometric algebra isomorphism. 相似文献
12.
Harris Kwong 《Discrete Mathematics》2008,308(23):5522-5532
Let G be a graph with vertex set V and edge set E, and let A be an abelian group. A labeling f:V→A induces an edge labeling f∗:E→A defined by f∗(xy)=f(x)+f(y). For i∈A, let vf(i)=card{v∈V:f(v)=i} and ef(i)=card{e∈E:f∗(e)=i}. A labeling f is said to be A-friendly if |vf(i)−vf(j)|≤1 for all (i,j)∈A×A, and A-cordial if we also have |ef(i)−ef(j)|≤1 for all (i,j)∈A×A. When A=Z2, the friendly index set of the graph G is defined as {|ef(1)−ef(0)|:the vertex labelingf is Z2-friendly}. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order n is cordial if and only if n?2 (mod 4). 相似文献
13.
We call A⊂RNintervally thin if for all x,y∈RN and ε>0 there exist x′∈B(x,ε), y′∈B(y,ε) such that [x′,y′]∩A=∅. Closed intervally thin sets behave like sets with measure zero (for example such a set cannot “disconnect” an open connected set). Let us also mention that if the (N−1)-dimensional Hausdorff measure of A is zero, then A is intervally thin. A function f is preconvex if it is convex on every convex subset of its domain. The consequence of our main theorem is the following: Let U be an open subset ofRNand let A be a closed intervally thin subset of U. Then every preconvex functioncan be uniquely extended (with preservation of preconvexity) onto U. In fact we show that a more general version of this result holds for semiconvex functions. 相似文献
14.
Mohammed Guedda 《Journal of Mathematical Analysis and Applications》2009,352(1):259-270
A multiplicity result for the singular ordinary differential equation y″+λx−2yσ=0, posed in the interval (0,1), with the boundary conditions y(0)=0 and y(1)=γ, where σ>1, λ>0 and γ?0 are real parameters, is presented. Using a logarithmic transformation and an integral equation method, we show that there exists Σ?∈(0,σ/2] such that a solution to the above problem is possible if and only if λγσ−1?Σ?. For 0<λγσ−1<Σ?, there are multiple positive solutions, while if γ=(λ−1Σ?)1/(σ−1) the problem has a unique positive solution which is monotonic increasing. The asymptotic behavior of y(x) as x→0+ is also given, which allows us to establish the absence of positive solution to the singular Dirichlet elliptic problem −Δu=d−2(x)uσ in Ω, where Ω⊂RN, N?2, is a smooth bounded domain and d(x)=dist(x,∂Ω). 相似文献
15.
Let R be a K-algebra acting densely on VD, where K is a commutative ring with unity and V is a right vector space over a division K-algebra D. Let ρ be a nonzero right ideal of R and let f(X1,…,Xt) be a nonzero polynomial over K with constant term 0 such that μR≠0 for some coefficient μ of f(X1,…,Xt). Suppose that d:R→R is a nonzero derivation. It is proved that if rankd(f(x1,…,xt))?m for all x1,…,xt∈ρ and for some positive integer m, then either ρ is generated by an idempotent of finite rank or d=ad(b) for some b∈End(VD) of finite rank. In addition, if f(X1,…,Xt) is multilinear, then b can be chosen such that rank(b)?2(6t+13)m+2. 相似文献
16.
Shih Ping Tung 《Journal of Number Theory》2010,130(4):912-929
In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z. 相似文献
17.
Yong-Soo Jung 《Journal of Mathematical Analysis and Applications》2008,339(1):108-114
Let A be a unital normed algebra and let M be a unitary Banach left A-module. If f:A→M is an approximate module left derivation, then f:A→M is a module left derivation. Moreover, if M=A is a semiprime unital Banach algebra and f(tx) is continuous in t∈R for each fixed x in A, then every approximately linear left derivation f:A→A is a linear derivation which maps A into the intersection of its center Z(A) and its Jacobson radical rad(A). In particular, if A is semisimple, then f is identically zero. 相似文献
18.
Emma D'Aniello 《Journal of Mathematical Analysis and Applications》2006,321(2):867-879
Let C be the collection of continuous self-maps of the unit interval I=[0,1] to itself. For f∈C and x∈I, let ω(x,f) be the ω-limit set of f generated by x, and following Block and Coppel, we take Q(x,f) to be the intersection of all the asymptotically stable sets of f containing ω(x,f). We show that Q(x,f) tells us quite a bit about the stability of ω(x,f) subject to perturbations of either x or f, or both. For example, a chain recurrent point y is contained in Q(x,f) if and only if there are arbitrarily small perturbations of f to a new function g that give us y as a point of ω(x,g). We also study the structure of the map Q taking (x,f)∈I×C to Q(x,f). We prove that Q is upper semicontinuous and a Baire 1 function, hence continuous on a residual subset of I×C. We also consider the map given by x?Q(x,f), and find that this map is continuous if and only if it is a constant map; that is, only when the set is a singleton. 相似文献
19.
20.
Hao ChengChu-Li Fu Xiao-Li Feng 《Journal of Computational and Applied Mathematics》2012,236(9):2582-2589
In this paper, we consider the problem of numerical analytic continuation of an analytic function f(z)=f(x+iy) on a strip domain Ω+={z=x+iy∈C∣x∈R,0<y<y0}, where the data is given approximately only on the real axis y=0. This problem is severely ill-posed: the solution does not depend continuously on the given data. A novel method (filtering) is used to solve this problem and an optimal error estimate with Hölder type is proved. Numerical examples show that this method works effectively. 相似文献