共查询到20条相似文献,搜索用时 31 毫秒
1.
P. Chansangiam 《Journal of Mathematical Analysis and Applications》2009,356(2):525-276
Let B(H) be the space of all bounded linear operators on a complex separable Hilbert space H. Bohr inequality for Hilbert space operators asserts that for A,B∈B(H) and p,q>1 real numbers such that 1/p+1/q=1,
2|A+B|?p2|A|+q2|B| 相似文献
2.
We show that a maximal curve over Fq2 given by an equation A(X)=F(Y), where A(X)∈Fq2[X] is additive and separable and where F(Y)∈Fq2[Y] has degree m prime to the characteristic p, is such that all roots of A(X) belong to Fq2. In the particular case where F(Y)=Ym, we show that the degree m is a divisor of q+1. 相似文献
3.
Let F be a field and let m and n be integers with m,n?3. Let Mn denote the algebra of n×n matrices over F. In this note, we characterize mappings ψ:Mn→Mm that satisfy one of the following conditions:
- 1.
- |F|=2 or |F|>n+1, and ψ(adj(A+αB))=adj(ψ(A)+αψ(B)) for all A,B∈Mn and α∈F with ψ(In)≠0.
- 2.
- ψ is surjective and ψ(adj(A-B))=adj(ψ(A)-ψ(B)) for every A,B∈Mn.
4.
Susana Furtado 《Linear algebra and its applications》2008,429(7):1663-1678
Let F be a field. In [Djokovic, Product of two involutions, Arch. Math. 18 (1967) 582-584] it was proved that a matrix A∈Fn×n can be written as A=BC, for some involutions B,C∈Fn×n, if and only if A is similar to A-1. In this paper we describe the possible eigenvalues of the matrices B and C.As a consequence, in case charF≠2, we describe the possible similarity classes of (P11⊕P22)P-1, when the nonsingular matrix P=[Pij]∈Fn×n, i,j∈{1,2} and P11∈Fs×s, varies.When F is an algebraically closed field and charF≠2, we also describe the possible similarity classes of [Aij]∈Fn×n, i,j∈{1,2}, when A11 and A22 are square zero matrices and A12 and A21 vary. 相似文献
5.
6.
Let p≥2 be an integer and T be an edge-weighted tree. A cut on an edge of T is a splitting of the edge at some point on it. A p-edge-partition of T is a set of p subtrees induced by p−1 cuts. Given p and T, the max-min continuous tree edge-partition problem is to find a p-edge-partition that maximizes the length of the smallest subtree; and the min-max continuous tree edge-partition problem is to find a p-edge-partition that minimizes the length of the largest subtree. In this paper, O(n2)-time algorithms are proposed for these two problems, improving the previous upper bounds by a factor of log (min{p,n}). Along the way, we solve a problem, named the ratio search problem. Given a positive integer m, a (non-ordered) set B of n non-negative real numbers, a real valued non-increasing function F, and a real number t, the problem is to find the largest number z in {b/a|a∈[1,m],b∈B} such that F(z)≥t. We give an O(n+tF×(logn+logm))-time algorithm for this problem, where tF is the time required to evaluate the function value F(z) for any real number z. 相似文献
7.
Sheng Chen 《Linear algebra and its applications》2009,431(8):1397-1406
In this paper the relation between the zeta function of an integral matrix and its generalized Bowen-Franks groups is studied. Suppose that A and B are nonnegative integral matrices whose invertible part is diagonalizable over the field of complex numbers and A and B have the same zeta function. Then there is an integer m, which depends only on the zeta function, such that, for any prime q such that gcd(q,m)=1, for any g(x)∈Z[x] with g(0)=1, the q-Sylow subgroup of the generalized Bowen-Franks group BFg(x)(A) and BFg(x)(B) are the same. In particular, if m=1, then zeta function determines generalized Bowen-Franks groups. 相似文献
8.
Omar Hirzallah 《Journal of Mathematical Analysis and Applications》2003,282(2):578-583
It is shown that if A, B, X are Hilbert space operators such that X?γI, for the positive real number γ, and p,q>1 with 1/p+1/q=1, then |A−B|2?p|A|2+q|B|2 with equality if and only if (1−p)A=B and γ||||A−B|2|||?|||p|A|2X+qX|B|2||| for every unitarily invariant norm. Moreover, if in addition A, B are normal and X is any Hilbert-Schmidt operator, then ‖δA,B2(X)‖2?‖p|A|2X+qX|B|2‖2 with equality if and only if (1−p)AX=XB. 相似文献
9.
Wolfgang Arendt 《Journal of Functional Analysis》2006,238(1):340-352
Let A be the generator of a cosine function on a Banach space X. In many cases, for example if X is a UMD-space, A+B generates a cosine function for each B∈L(D((ω−A)1/2),X). If A is unbounded and , then we show that there exists a rank-1 operator B∈L(D(γ(ω−A)),X) such that A+B does not generate a cosine function. The proof depends on a modification of a Baire argument due to Desch and Schappacher. It also allows us to prove the following. If A+B generates a distribution semigroup for each operator B∈L(D(A),X) of rank-1, then A generates a holomorphic C0-semigroup. If A+B generates a C0-semigroup for each operator B∈L(D(γ(ω−A)),X) of rank-1 where 0<γ<1, then the semigroup T generated by A is differentiable and ‖T′(t)‖=O(t−α) as t↓0 for any α>1/γ. This is an approximate converse of a perturbation theorem for this class of semigroups. 相似文献
10.
A.B. Aleksandrov 《Journal of Functional Analysis》2010,258(11):3675-5251
This is a continuation of our paper [2]. We prove that for functions f in the Hölder class Λα(R) and 1<p<∞, the operator f(A)−f(B) belongs to Sp/α, whenever A and B are self-adjoint operators with A−B∈Sp. We also obtain sharp estimates for the Schatten-von Neumann norms ‖f(A)−f(B)Sp/α‖ in terms of ‖A−BSp‖ and establish similar results for other operator ideals. We also estimate Schatten-von Neumann norms of higher order differences . We prove that analogous results hold for functions on the unit circle and unitary operators and for analytic functions in the unit disk and contractions. Then we find necessary conditions on f for f(A)−f(B) to belong to Sq under the assumption that A−B∈Sp. We also obtain Schatten-von Neumann estimates for quasicommutators f(A)R−Rf(B), and introduce a spectral shift function and find a trace formula for operators of the form f(A−K)−2f(A)+f(A+K). 相似文献
11.
Alan Horwitz 《Journal of Mathematical Analysis and Applications》2002,267(2):489-500
Let F ⊂ K be fields of characteristic 0, and let K[x] denote the ring of polynomials with coefficients in K. Let p(x) = ∑k = 0nakxk ∈ K[x], an ≠ 0. For p ∈ K[x]\F[x], define DF(p), the F deficit of p, to equal n − max{0 ≤ k ≤ n : ak∉F}. For p ∈ F[x], define DF(p) = n. Let p(x) = ∑k = 0nakxk and let q(x) = ∑j = 0mbjxj, with an ≠ 0, bm ≠ 0, an, bm ∈ F, bj∉F for some j ≥ 1. Suppose that p ∈ K[x], q ∈ K[x]\F[x], p, not constant. Our main result is that p ° q ∉ F[x] and DF(p ° q) = DF(q). With only the assumption that anbm ∈ F, we prove the inequality DF(p ° q) ≥ DF(q). This inequality also holds if F and K are only rings. Similar results are proven for fields of finite characteristic with the additional assumption that the characteristic of the field does not divide the degree of p. Finally we extend our results to polynomials in two variables and compositions of the form p(q(x, y)), where p is a polynomial in one variable. 相似文献
12.
B.P. Duggal 《Linear algebra and its applications》2008,428(4):1109-1116
A Hilbert space operator A∈B(H) is p-hyponormal, A∈(p-H), if |A∗|2p?|A|2p; an invertible operator A∈B(H) is log-hyponormal, A∈(?-H), if log(TT∗)?log(T∗T). Let dAB=δAB or ?AB, where δAB∈B(B(H)) is the generalised derivation δAB(X)=AX-XB and ?AB∈B(B(H)) is the elementary operator ?AB(X)=AXB-X. It is proved that if A,B∗∈(?-H)∪(p-H), then, for all complex λ, , the ascent of (dAB-λ)?1, and dAB satisfies the range-kernel orthogonality inequality ‖X‖?‖X-(dAB-λ)Y‖ for all X∈(dAB-λ)-1(0) and Y∈B(H). Furthermore, isolated points of σ(dAB) are simple poles of the resolvent of dAB. A version of the elementary operator E(X)=A1XA2-B1XB2 and perturbations of dAB by quasi-nilpotent operators are considered, and Weyl’s theorem is proved for dAB. 相似文献
13.
Xiaofei Song 《Linear algebra and its applications》2008,429(7):1579-1586
Let Mn be the algebra of all n×n complex matrices and Γn the set of all k-potent matrices in Mn. Suppose ?:Mn→Mn is a map satisfying A-λB∈Γn implies ?(A)-λ?(B)∈Γn, where A, B∈Mn, λ∈C. Then either ? is of the form ?(A)=cTAT-1, A∈Mn, or ? is of the form ?(A)=cTAtT-1, A∈Mn, where T∈Mn is an invertible matrix, c∈C satisfies ck=c. 相似文献
14.
Lu Yang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):3876-3883
In this paper, we study the long-time behavior of the reaction-diffusion equation with dynamical boundary condition, where the nonlinear terms f and g satisfy the polynomial growth condition of arbitrary order. Some asymptotic regularity of the solution has been proved. As an application of the asymptotic regularity results, we can not only obtain the existence of a global attractor A in (H1(Ω)∩Lp(Ω))×Lq(Γ) immediately, but also can show further that A attracts every L2(Ω)×L2(Γ)-bounded subset with (H1(Ω)∩Lp+δ(Ω))×Lq+κ(Γ)-norm for any δ,κ∈[0,∞). 相似文献
15.
Irene Benedetti Luisa Malaguti Valentina Taddei 《Journal of Mathematical Analysis and Applications》2010,368(1):90-102
The paper deals with the multivalued initial value problem x′∈A(t,x)x+F(t,x) for a.a. t∈[a,b], x(a)=x0 in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x and the investigation includes the case when both A and F have a superlinear growth in x. We prove the existence of local and global classical solutions in the Sobolev space W1,p([a,b],E) with 1<p<∞. Introducing a suitably defined Lyapunov-like function, we are able to investigate the topological structure of the solution set. Our main tool is a continuation principle in Frechét spaces and we prove the required pushing condition in two different ways. Some examples complete the discussion. 相似文献
16.
Donald Mills 《Journal of Number Theory》2002,92(1):87-98
Let Fq denote the finite field of q elements, q=pe odd, let χ1 denote the canonical additive character of Fq where χ1(c)=e2πiTr(c)/p for all c∈Fq, and let Tr represent the trace function from Fq to Fp. We are interested in evaluating Weil sums of the form S=S(a1, …, an)=∑x∈Fq χ1(D(x)) where D(x)=∑ni=1 aixpαi+pβi, αi?βi for each i, is known as a Dembowski-Ostrom polynomial (or as a D-O polynomial). Coulter has determined the value of S when D(x)=axpα+1; in this note we show how Coulter's methods can be generalized to determine the absolute value of S for any D-O polynomial. When e is even, we give a subclass of D-O polynomials whose Weil sums are real-valued, and in certain cases we are able to resolve the sign of S. We conclude by showing how Coulter's work for the monomial case can be used to determine a lower bound on the number of Flq-solutions to the diagonal-type equation ∑li=1 xpγ+1i+(xi+λ)pγ+1=0, where l is even, e/gcd(γ, e) is odd, and h (X)=λpe−γXpe−γ+λpγX is a permutation polynomial over Fq. 相似文献
17.
We propose a new characterization of dual bases in finite fields. Let A=(α1,…,αn) be a basis of F over Fq and its dual basis B=(β1,…,βn) with the transition matrix C∈GLn(Fq) such that (β1,…,βn)=(α1,…,αn)C. We show that holds for all 1?k?n, where Tk∈Mn(Fq) satisfies αk(α1,…,αn)=(α1,…,αn)Tk. Conversely, suppose F=Fq(αk′) and for some 1?k′?n and G∈GLn(Fq), then B is equivalent to (α1,…,αn)G. As applications, we can construct the dual basis of a given basis A or determine whether the dual basis of A satisfies the desired conditions from Tk. This generalizes the results obtained by Liao and Sun for normal bases. Furthermore, we give a simple proof of the theorem of Gollmann, Wang and Blake for polynomial bases. 相似文献
18.
Wen Zhang 《Linear algebra and its applications》2011,435(6):1326-1335
Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y, respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is the set σπ(A)={z∈σ(A):|z|=maxω∈σ(A)|ω|}, where σ(A) denotes the spectrum of A. Assume that Φ:A→B is a map the range of which contains all operators of rank at most two. It is shown that the map Φ satisfies the condition that σπ(BAB)=σπ(Φ(B)Φ(A)Φ(B)) for all A,B∈A if and only if there exists a scalar λ∈C with λ3=1 and either there exists an invertible operator T∈B(X,Y) such that Φ(A)=λTAT-1 for every A∈A; or there exists an invertible operator T∈B(X∗,Y) such that Φ(A)=λTA∗T-1 for every A∈A. If X=H and Y=K are complex Hilbert spaces, the maps preserving the peripheral spectrum of the Jordan skew semi-triple product BA∗B are also characterized. Such maps are of the form A?UAU∗ or A?UAtU∗, where U∈B(H,K) is a unitary operator, At denotes the transpose of A in an arbitrary but fixed orthonormal basis of H. 相似文献
19.
Let F denote a finite field with q=pf elements, and let σ(A) equal the trace of the square matrix A. This paper evaluates exponential sums of the form S(E,X1,…,Xn)e{?σ(CX1?XnE)}, where S(E,X1,…,Xn) denotes a summation over all matrices E,X1,…,Xn of appropriate sizes over F, and C is a fixed matrix. This evaluation is then applied to the problem of counting ranked solutions to matrix equations of the form U1?UαA+DV1?Vβ=B where A,B,D are fixed matrices over F. 相似文献
20.
Let F be a family of subsets of a finite set V. The star ofFatv∈V is the sub-family {A∈F:v∈A}. We denote the sub-family {A∈F:|A|=r} by F(r).A double partitionP of a finite set V is a partition of V into large sets that are in turn partitioned into small sets. Given such a partition, the family F(P)induced byP is the family of subsets of V whose intersection with each large set is either contained in just one small set or empty.Our main result is that, if one of the large sets is trivially partitioned (that is, into just one small set) and 2r is not greater than the least cardinality of any maximal set of F(P), then no intersecting sub-family of F(P)(r) is larger than the largest star of F(P)(r). We also characterise the cases when every extremal intersecting sub-family of F(P)(r) is a star of F(P)(r). 相似文献