共查询到20条相似文献,搜索用时 109 毫秒
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Chi-Kwong Li 《Linear algebra and its applications》2009,431(12):2336-2345
Let B(H) be the algebra of bounded linear operator acting on a Hilbert space H (over the complex or real field). Characterization is given to A1,…,Ak∈B(H) such that for any unitary operators is always in a special class S of operators such as normal operators, self-adjoint operators, unitary operators. As corollaries, characterizations are given to A∈B(H) such that complex, real or nonnegative linear combinations of operators in its unitary orbit U(A)={U∗AU:Uunitary} always lie in S. 相似文献
3.
Pierrette Cassou-Noguès 《Journal of Pure and Applied Algebra》2009,213(5):711-723
Let φ=(f,g) be an endomorphism of the affine plane C2 defined by two polynomials f,g∈C[x,y] and let Λ={Cb∣b∈C} be the pencil of lines Cb defined by x=b. We shall consider the smoothness criterion of the image curve φ(Cb). The hypersurface V whose coordinate ring is C[x,f,g] and the normalization of V will play interesting roles in analyzing the properties of the set φ(Λ)={φ(Cb)∣b∈C}. 相似文献
4.
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
5.
Suk-Geun Hwang 《Linear algebra and its applications》2011,434(2):475-479
A family F of square matrices of the same order is called a quasi-commuting family if (AB-BA)C=C(AB-BA) for all A,B,C∈F where A,B,C need not be distinct. Let fk(x1,x2,…,xp),(k=1,2,…,r), be polynomials in the indeterminates x1,x2,…,xp with coefficients in the complex field C, and let M1,M2,…,Mr be n×n matrices over C which are not necessarily distinct. Let and let δF(x1,x2,…,xp)=detF(x1,x2,…,xp). In this paper, we prove that, for n×n matrices A1,A2,…,Ap over C, if {A1,A2,…,Ap,M1,M2,…,Mr} is a quasi-commuting family, then F(A1,A2,…,Ap)=O implies that δF(A1,A2,…,Ap)=O. 相似文献
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Let [n] denote the set of positive integers {1,2,…,n}. An r-partial permutation of [n] is a pair (A,f) where A⊆[n], |A|=r and f:A→[n] is an injective map. A set A of r-partial permutations is intersecting if for any (A,f), (B,g)∈A, there exists x∈A∩B such that f(x)=g(x). We prove that for any intersecting family A of r-partial permutations, we have .It seems rather hard to characterize the case of equality. For 8?r?n-3, we show that equality holds if and only if there exist x0 and ε0 such that A consists of all (A,f) for which x0∈A and f(x0)=ε0. 相似文献
7.
Maria Monks 《Discrete Mathematics》2009,309(16):5196-1883
All continuous endomorphisms f∞ of the shift dynamical system S on the 2-adic integers Z2 are induced by some , where n is a positive integer, Bn is the set of n-blocks over {0, 1}, and f∞(x)=y0y1y2… where for all i∈N, yi=f(xixi+1…xi+n−1). Define D:Z2→Z2 to be the endomorphism of S induced by the map {(00,0),(01,1),(10,1),(11,0)} and V:Z2→Z2 by V(x)=−1−x. We prove that D, V°D, S, and V°S are conjugate to S and are the only continuous endomorphisms of S whose parity vector function is solenoidal. We investigate the properties of D as a dynamical system, and use D to construct a conjugacy from the 3x+1 function T:Z2→Z2 to a parity-neutral dynamical system. We also construct a conjugacy R from D to T. We apply these results to establish that, in order to prove the 3x+1 conjecture, it suffices to show that for any m∈Z+, there exists some n∈N such that R−1(m) has binary representation of the form or . 相似文献
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Fang Jia 《Differential Geometry and its Applications》2005,22(2):199-214
Let be a locally strongly convex hypersurface, given by a strictly convex function xn+1=f(x1,…,xn) defined in a convex domain Ω⊂An. We consider the Riemannian metric G# on M, defined by . In this paper we prove that if M is a locally strongly convex surface with constant affine mean curvature and if M is complete with respect to the metric G#, then M must be an elliptic paraboloid. 相似文献
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In this paper we are interested in the existence of solutions of the following initial value problem: on (0,T) with u(0)=u0 where A:V→V′ is a monotone operator, G:V→V′ is a nonlinear nonmonotone operator and f:(0,T)→V′ is a measurable function, by means of a recent generalization of the famous KKM-Fan’s lemma. 相似文献
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Let Un ⊂ Cn[a, b] be an extended Chebyshev space of dimension n + 1. Suppose that f0 ∈ Un is strictly positive and f1 ∈ Un has the property that f1/f0 is strictly increasing. We search for conditions ensuring the existence of points t0, …, tn ∈ [a, b] and positive coefficients α0, …, αn such that for all f ∈ C[a, b], the operator Bn:C[a, b] → Un defined by satisfies Bnf0 = f0 and Bnf1 = f1. Here it is assumed that pn,k, k = 0, …, n, is a Bernstein basis, defined by the property that each pn,k has a zero of order k at a and a zero of order n − k at b. 相似文献
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Li Qiu 《Linear algebra and its applications》2007,422(1):304-307
Let A1, … , Ak be positive semidefinite matrices and B1, … , Bk arbitrary complex matrices of order n. We show that
span{(A1x)°(A2x)°?°(Akx)|x∈Cn}=range(A1°A2°?°Ak) 相似文献
12.
Singular values, norms, and commutators 总被引:1,自引:0,他引:1
Omar Hirzallah 《Linear algebra and its applications》2010,432(5):1322-1336
Let and Xi, i=1,…,n, be bounded linear operators on a separable Hilbert space such that Xi is compact for i=1,…,n. It is shown that the singular values of are dominated by those of , where ‖·‖ is the usual operator norm. Among other applications of this inequality, we prove that if A and B are self-adjoint operators such that a1?A?a2 and b1?B?b2 for some real numbers and b2, and if X is compact, then the singular values of the generalized commutator AX-XB are dominated by those of max(b2-a1,a2-b1)(X⊕X). This inequality proves a recent conjecture concerning the singular values of commutators. Several inequalities for norms of commutators are also given. 相似文献
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J.A. De Loera R. Hemmecke S. Onn U.G. Rothblum R. Weismantel 《Journal of Pure and Applied Algebra》2009,213(8):1569-1577
We present a new algebraic algorithmic scheme to solve convex integer maximization problems of the following form, where c is a convex function on Rd and w1x,…,wdx are linear forms on Rn,
max{c(w1x,…,wdx):Ax=b,x∈Nn}. 相似文献
14.
Peter C. Fishburn 《Mathematical Social Sciences》1981,1(2):145-153
Let ? be a binary relation on A×X, and suppose that there are real valued functions f on A and g on X such that, for all ax, by ∈ A×X, ax ? by if and only if f (a)+g(x) ? f(b)+g(y). This paper establishes uniqueness properties for f and g when A is a finite set, X is a real interval with g increasing on X, and for any a, b and x there is a y for which f(a)+g(x)=f(b)+g(y). The resultant uniqueness properties occupy an intermediate position among uniqueness properties for other structural cases of two-factor additive measurement.It is shown that f is unique up to a positive affine transformation (αf+β1 with α > 0), but that g is unique up to a similar positive affine transformation (αg+β2) if and only if the ratio [f(a)?f(b)]/[f(a)?f(c)] is irrational for some a, b, c ∈ A. When the f ratios are rational for all cases where they are defined, there will be a half-open interval (x0, x1) in X such that the restriction of g on (x0, x1) can be any increasing function for which sup {g(x)?g(x0): x0 ? x < x1} does not exceed a specified bound, and, when g is thus defines on (x0, x1), it will be uniquely determined on the rest of X. In general, g must be continuous only in the ‘irrational’ case. 相似文献
15.
G. Sampson 《Journal of Mathematical Analysis and Applications》2007,334(1):196-205
For aj,bj?1, j=1,2,…,d, we prove that the operator maps into itself for , where , and k(x,y)=φ(x,y)eig(x,y), φ(x,y) satisfies (1.2) (e.g. φ(x,y)=|x−y|iτ,τ real) and the phase g(x,y)=xa⋅yb. We study operators with more general phases and for these operators we require that aj,bj>1, j=1,2,…,d, or al=bl?1 for some l∈{1,2,…,d}. 相似文献
16.
Let Cp be the Schatten p-class for p>0. Generalizations of the parallelogram law for the Schatten 2-norms have been given in the following form: if A={A1,A2,…,An} and B={B1,B2,…,Bn} are two sets of operators in, then C2
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Let A and B be commutative rings with identity, f:A→B a ring homomorphism and J an ideal of B . Then the subring A?fJ:={(a,f(a)+j)|a∈A and j∈J} of A×B is called the amalgamation of A with B along with J with respect to f. In this paper, we investigate a general concept of the Noetherian property, called the S -Noetherian property which was introduced by Anderson and Dumitrescu, on the ring A?fJ for a multiplicative subset S of A?fJ. As particular cases of the amalgamation, we also devote to study the transfers of the S -Noetherian property to the constructions D+(X1,…,Xn)E[X1,…,Xn] and D+(X1,…,Xn)E?X1,…,Xn? and Nagata?s idealization. 相似文献
18.
S.W. Drury 《Linear algebra and its applications》2007,422(1):318-325
We establish the following case of the Determinantal Conjecture of Marcus [M. Marcus, Derivations, Plücker relations and the numerical range, Indiana Univ. Math. J. 22 (1973) 1137-1149] and de Oliveira [G.N. de Oliveira, Research problem: Normal matrices, Linear and Multilinear Algebra 12 (1982) 153-154]. Let A and B be unitary n × n matrices with prescribed eigenvalues a1, … , an and b1, … , bn, respectively. Then for any scalars t and s
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V.V. Bavula 《Journal of Pure and Applied Algebra》2008,212(10):2320-2337
Let K be an arbitrary field of characteristic p>0. We find an explicit formula for the inverse of any algebra automorphism of any of the following algebras: the polynomial algebra Pn?K[x1,…,xn], the ring of differential operators D(Pn) on Pn, D(Pn)⊗Pm, the n’th Weyl algebra An or An⊗Pm, the power series algebra K[[x1,…,xn]], the subalgebra Tk1,…,kn of D(Pn) generated by Pn and the higher derivations , 0≤j<pki, i=1,…,n (where k1,…,kn∈N), Tk1,…,kn⊗Pm or an arbitrary central simple (countably generated) algebra over an arbitrary field. 相似文献
20.
Dorothee D. Haroske Leszek Skrzypczak 《Journal of Mathematical Analysis and Applications》2010,371(1):282-299
This paper is based on our previous results (Haroske and Skrzypczak (2008) [23], Haroske and Skrzypczak (in press) [25]) on compact embeddings of Muckenhoupt weighted function spaces of Besov and Triebel-Lizorkin type with example weights of polynomial growth near infinity and near some local singularity. Our approach also extends (Haroske and Triebel (1994) [21]) in various ways. We obtain eigenvalue estimates of degenerate pseudodifferential operators of type b2○p(x,D)○b1 where bi∈Lri(Rn,wi), wi∈A∞, i=1,2, and , ?>0. Finally we deal with the ‘negative spectrum’ of some operator Hγ=A−γV for γ→∞, where the potential V may have singularities (in terms of Muckenhoupt weights), and A is a positive elliptic pseudodifferential operator of order ?>0, self-adjoint in L2(Rn). This part essentially relies on the Birman-Schwinger principle. We conclude this paper with a number of examples, also comparing our results with preceding ones. 相似文献